Document Zbl 07966982

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Control Optim.</a> <a href="/?q=in%3A522516" title="Articles in this Issue">63, No. 1, 26-56 (2025)</a>. </div> <div class="abstract"><div class="pre">Summary: In this paper, we present an impulse response identification scheme that incorporates the internal positivity side-information of the system. The realization theory of positive systems establishes specific criteria for the existence of a positive realization for a given transfer function. These transfer function criteria are translated to a set of suitable conditions on the shape and structure of the impulse responses of positive systems. Utilizing these conditions, the impulse response estimation problem is formulated as a constrained optimization in a reproducing kernel Hilbert space equipped with a stable kernel, and suitable constraints are imposed to encode the internal positivity side-information. The optimization problem is infinite-dimensional with an infinite number of constraints. An equivalent finite-dimensional convex optimization in the form of a convex quadratic program is derived. The resulting equivalent reformulation makes the proposed approach suitable for numerical simulation and practical implementation. A Monte Carlo numerical experiment evaluates the impact of incorporating the internal positivity side-information in the proposed identification scheme. The effectiveness of the proposed method is demonstrated using data from a heating system experiment.</div></div> <div class="clear"></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A93B30" title="MSC2020">93B30</a> </td> <td class="space"> System identification </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C28" title="MSC2020">93C28</a> </td> <td class="space"> Positive control/observation systems </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A93C25" title="MSC2020">93C25</a> </td> <td class="space"> Control/observation systems in abstract spaces </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A46E22" title="MSC2020">46E22</a> </td> <td class="space"> Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Asystem+identification">system identification</a>; <a href="/?q=ut%3Apositive+systems">positive systems</a>; <a href="/?q=ut%3Akernel+methods">kernel methods</a></div> <div class="software"> <h3>Software:</h3><a href="/software/4594">CVX</a>; <a href="/software/27194">IPsolve</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 07966982" data-ciurl="/ci/07966982" data-biburl="/bibtex/07966982.bib" data-amsurl="/amsrefs/07966982.bib" data-xmlurl="/xml/07966982.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07966982.pdf" title="Zbl 07966982 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1137/23M1556095" aria-label="DOI for “Regularized identification with internal positivity side-information”" title="10.1137/23M1556095">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2111.00407" title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Ahmadi, A. A. and El Khadir, B., Learning dynamical systems with side information (short version), Proc. Mach. Learn. Res., 120 (2020), pp. 718-727, http://proceedings.mlr.press/v120/ahmadi20a.</td> </tr><tr> <td>[2]</td> <td class="space">Aravkin, A. Y., Burke, J. V., and Pillonetto, G., Generalized system identification with stable spline kernels, SIAM J. Sci. Comput., 40 (2018), pp. B1419-B1443, doi:10.1137/16M1070517. · <a href="/1404.62051" class="nowrap">Zbl 1404.62051</a></td> </tr><tr> <td>[3]</td> <td class="space">Back, J. and Astolfi, A., Design of positive linear observers for positive linear systems via coordinate transformations and positive realizations, SIAM J. Control Optim., 47 (2008), pp. 345-373, doi:10.1137/060663891. · <a href="/1157.93009" class="nowrap">Zbl 1157.93009</a></td> </tr><tr> <td>[4]</td> <td class="space">Bellman, R., Dynamic programming, system identification, and suboptimization, SIAM J. Control, 4 (1966), pp. 1-5, doi:10.1137/0304001. · <a href="/0201.47902" class="nowrap">Zbl 0201.47902</a></td> </tr><tr> <td>[5]</td> <td class="space">Benvenuti, L., De Santis, A., and Farina, L., On model consistency in compartmental systems identification, Automatica, 38 (2002), pp. 1969-1976, doi:10.1016/S0005-1098(02)00107-3. · <a href="/1011.93027" class="nowrap">Zbl 1011.93027</a></td> </tr><tr> <td>[6]</td> <td class="space">Benvenuti, L. and Farina, L., A tutorial on the positive realization problem, IEEE Trans. Automat. Control, 49 (2004), pp. 651-664, doi:10.1109/TAC.2004.826715. · <a href="/1365.93001" class="nowrap">Zbl 1365.93001</a></td> </tr><tr> <td>[7]</td> <td class="space">Berlinet, A. and Thomas-Agnan, C., Reproducing Kernel Hilbert Spaces in Probability and Statistics, Springer, Cham, 2011.</td> </tr><tr> <td>[8]</td> <td class="space">Bisiacco, M. and Pillonetto, G., Kernel absolute summability is sufficient but not necessary for RKHS stability, SIAM J. Control Optim., 58 (2020), pp. 2006-2022, doi:10.1137/19M1278442. · <a href="/1445.47056" class="nowrap">Zbl 1445.47056</a></td> </tr><tr> <td>[9]</td> <td class="space">Brown, R. F., Compartmental system analysis: State of the art, IEEE Trans. Bio-Mec. Eng., BME-27 (1980), pp. 1-11, doi:10.1109/TBME.1980.326685.</td> </tr><tr> <td>[10]</td> <td class="space">Chen, T., On kernel design for regularized LTI system identification, Automatica, 90 (2018), pp. 109-122, doi:10.1016/j.automatica.2017.12.039. · <a href="/1387.93064" class="nowrap">Zbl 1387.93064</a></td> </tr><tr> <td>[11]</td> <td class="space">Chen, T., Ohlsson, H., and Ljung, L., On the estimation of transfer functions, regularizations and Gaussian processes - Revisited, Automatica, 48 (2012), pp. 1525-1535, doi:10.1016/j.automatica.2012.05.026. · <a href="/1269.93126" class="nowrap">Zbl 1269.93126</a></td> </tr><tr> <td>[12]</td> <td class="space">Chen, T. and Pillonetto, G., On the stability of reproducing kernel Hilbert spaces of discrete-time impulse responses, Automatica, 95 (2018), pp. 529-533, doi:10.1016/j.automatica.2018.05.017. · <a href="/1402.93091" class="nowrap">Zbl 1402.93091</a></td> </tr><tr> <td>[13]</td> <td class="space">Colombino, M. and Smith, R. S., A convex characterization of robust stability for positive and positively dominated linear systems, IEEE Trans. Automat. Control, 61 (2015), pp. 1965-1971, doi:10.1109/TAC.2015.2480549. · <a href="/1359.93349" class="nowrap">Zbl 1359.93349</a></td> </tr><tr> <td>[14]</td> <td class="space">Darwish, M. A. H., Pillonetto, G., and Tóth, R., The quest for the right kernel in Bayesian impulse response identification: The use of OBFs, Automatica, 87 (2018), pp. 318-329, doi:10.1016/j.automatica.2017.10.007. · <a href="/1378.93130" class="nowrap">Zbl 1378.93130</a></td> </tr><tr> <td>[15]</td> <td class="space">De Moor, B., De Gersem, P., De Schutter, B., and Favoreel, W., DAISY: A database for identification of systems, J. A, 38 (1997), pp. 4-5.</td> </tr><tr> <td>[16]</td> <td class="space">De Santis, A. and Farina, L., Identification of positive linear systems with Poisson output transformation, Automatica, 38 (2002), pp. 861-868, doi:10.1016/S0005-1098(01)00277-1. · <a href="/1030.93008" class="nowrap">Zbl 1030.93008</a></td> </tr><tr> <td>[17]</td> <td class="space">Dhingra, N. K., Colombino, M., and Jovanović, M. R., Structured decentralized control of positive systems with applications to combination drug therapy and leader selection in directed networks, IEEE Trans. Control Network Syst., 6 (2018), pp. 352-362, doi:10.1109/TCNS.2018.2820499. · <a href="/1515.93016" class="nowrap">Zbl 1515.93016</a></td> </tr><tr> <td>[18]</td> <td class="space">Dinuzzo, F., Kernels for linear time invariant system identification, SIAM J. Control Optim., 53 (2015), pp. 3299-3317, doi:10.1137/130920319. · <a href="/1329.93049" class="nowrap">Zbl 1329.93049</a></td> </tr><tr> <td>[19]</td> <td class="space">Dinuzzo, F. and Schölkopf, B., The representer theorem for Hilbert spaces: A necessary and sufficient condition, in Advances in Neural Information Processing Systems 2012, 2012, pp. 189-196.</td> </tr><tr> <td>[20]</td> <td class="space">Duan, X., Jafarpour, S., and Bullo, F., Graph-theoretic stability conditions for Metzler matrices and monotone systems, SIAM J. Control Optim., 59 (2021), pp. 3447-3471, doi:10.1137/20M131802X. · <a href="/1472.93143" class="nowrap">Zbl 1472.93143</a></td> </tr><tr> <td>[21]</td> <td class="space">Dullerud, G. and Smith, R., Sampled-data model validation: An algorithm and experimental application, Int. J. Robust Nonlinear Control, 6 (1996), pp. 1065-1078, doi:10.1002/(SICI)1099-1239(199611)6:9/10<1065::AID-RNC269>3.0.CO;2-N. · <a href="/0875.93266" class="nowrap">Zbl 0875.93266</a></td> </tr><tr> <td>[22]</td> <td class="space">Ebihara, Y., Peaucelle, D., and Arzelier, D., Decentralized control of interconnected positive systems using L1-induced norm characterization, in 2012 IEEE 51st IEEE Conference on Decision and Control (CDC), , IEEE, 2012, pp. 6653-6658.</td> </tr><tr> <td>[23]</td> <td class="space">Ebihara, Y., Peaucelle, D., and Arzelier, D., Stability and persistence analysis of large scale interconnected positive systems, in 2013 European Control Conference (ECC), , IEEE, 2013, pp. 3366-3371.</td> </tr><tr> <td>[24]</td> <td class="space">Everitt, N., Bottegal, G., and Hjalmarsson, H., An empirical Bayes approach to identification of modules in dynamic networks, Automatica, 91 (2018), pp. 144-151, doi:10.1016/j.automatica.2018.01.011. · <a href="/1387.93165" class="nowrap">Zbl 1387.93165</a></td> </tr><tr> <td>[25]</td> <td class="space">Farina, L. and Rinaldi, S., Positive Linear Systems: Theory and Applications, Wiley, Hoboken, NJ, 2011.</td> </tr><tr> <td>[26]</td> <td class="space">Fornasini, E. and Valcher, M. E., Reachability of a class of discrete-time positive switched systems, SIAM J. Control Optim., 49 (2011), pp. 162-184, doi:10.1137/090757551. · <a href="/1215.93017" class="nowrap">Zbl 1215.93017</a></td> </tr><tr> <td>[27]</td> <td class="space">Fuhrmann, P. A., A Polynomial Approach to Linear Algebra, Springer, Cham, 2011.</td> </tr><tr> <td>[28]</td> <td class="space">Fujimoto, Y., Maruta, I., and Sugie, T., Extension of first-order stable spline kernel to encode relative degree, IFAC-PapersOnLine, 50 (2017), pp. 14016-14021, doi:10.1016/j.ifacol.2017.08.2425.</td> </tr><tr> <td>[29]</td> <td class="space">Gondzio, J., González-Brevis, P., and Munari, P., Large-scale optimization with the primal-dual column generation method, Math. Program. Comput., 8 (2016), pp. 47-82, doi:10.1007/s12532-015-0090-6. · <a href="/1334.90072" class="nowrap">Zbl 1334.90072</a></td> </tr><tr> <td>[30]</td> <td class="space">Grant, M. and Boyd, S., CVX: Matlab Software for Disciplined Convex Programming, version 2.1, 2014, https://cvxr.com/cvx/.</td> </tr><tr> <td>[31]</td> <td class="space">Grussler, C. and Rantzer, A., On second-order cone positive systems, SIAM J. Control Optim., 59 (2021), pp. 2717-2739, doi:10.1137/20M1337454. · <a href="/1470.93075" class="nowrap">Zbl 1470.93075</a></td> </tr><tr> <td>[32]</td> <td class="space">Grussler, C., Umenberger, J., and Manchester, I. R., Identification of externally positive systems, in 2017 IEEE 56th Annual Conference on Decision and Control, , IEEE, 2017, pp. 6549-6554.</td> </tr><tr> <td>[33]</td> <td class="space">Haddad, W. M., Chellaboina, V., and Hui, Q., Nonnegative and Compartmental Dynamical Systems, Princeton University Press, Princeton, NJ, 2010. · <a href="/1184.93001" class="nowrap">Zbl 1184.93001</a></td> </tr><tr> <td>[34]</td> <td class="space">Hinrichsen, D. and Plischke, E., Robust stability and transient behaviour of positive linear systems, Vietnam J. Math., 35 (2007), pp. 429-462. · <a href="/1330.93184" class="nowrap">Zbl 1330.93184</a></td> </tr><tr> <td>[35]</td> <td class="space">Khosravi, M., Representer theorem for learning Koopman operators, IEEE Trans. Automat. Control, 68 (2023), pp. 2995-3010, doi:10.1109/TAC.2023.3242325. · <a href="/1546.93121" class="nowrap">Zbl 1546.93121</a></td> </tr><tr> <td>[36]</td> <td class="space">Khosravi, M., Iannelli, A., Yin, M., Parsi, A., and Smith, R. S., Regularized system identification: A hierarchical Bayesian approach, IFAC-PapersOnLine, 53 (2020), pp. 406-411.</td> </tr><tr> <td>[37]</td> <td class="space">Khosravi, M. and Smith, R. S., Kernel-based identification of positive systems, in 2019 IEEE 58th Annual Conference on Decision and Control, , IEEE, 2019, pp. 1740-1745, doi:10.1109/CDC40024.2019.9029276.</td> </tr><tr> <td>[38]</td> <td class="space">Khosravi, M. and Smith, R. S., Convex nonparametric formulation for identification of gradient flows, IEEE Control Syst. Lett., 5 (2021), pp. 1097-1102, doi:10.1109/LCSYS.2020.3000176.</td> </tr><tr> <td>[39]</td> <td class="space">Khosravi, M. and Smith, R. S., Nonlinear system identification with prior knowledge on the region of attraction, IEEE Control Syst. Lett., 5 (2021), pp. 1091-1096, doi:10.1109/LCSYS.2020.3005163.</td> </tr><tr> <td>[40]</td> <td class="space">Khosravi, M. and Smith, R. S., On robustness of kernel-based regularized system identification, IFAC-PapersOnLine, 54 (2021), pp. 749-754.</td> </tr><tr> <td>[41]</td> <td class="space">Khosravi, M. and Smith, R. S., Diagonally Square Root Integrable Kernels in System Identification, preprint, arXiv:2302.12929, 2023.</td> </tr><tr> <td>[42]</td> <td class="space">Khosravi, M. and Smith, R. S., The existence and uniqueness of solutions for kernel-based system identification, Automatica, 148 (2023), 110728, doi:10.1016/j.automatica.2022.110728. · <a href="/1507.93053" class="nowrap">Zbl 1507.93053</a></td> </tr><tr> <td>[43]</td> <td class="space">Khosravi, M. and Smith, R. S., Kernel-based identification with frequency domain side-information, Automatica, 150 (2023), 110813, doi:10.1016/j.automatica.2022.110813. · <a href="/1528.93030" class="nowrap">Zbl 1528.93030</a></td> </tr><tr> <td>[44]</td> <td class="space">Khosravi, M. and Smith, R. S., Kernel-based impulse response identification with side-information on steady-state gain, IEEE Trans. Automat. Control, 68 (2023), pp. 6401-6408, doi:10.1109/TAC.2023.3243099. · <a href="/1546.93122" class="nowrap">Zbl 1546.93122</a></td> </tr><tr> <td>[45]</td> <td class="space">Khosravi, M., Yin, M., Iannelli, A., Parsi, A., and Smith, R. S., Low-complexity identification by sparse hyperparameter estimation, IFAC-PapersOnLine, 53 (2020), pp. 412-417.</td> </tr><tr> <td>[46]</td> <td class="space">Krause, U., Positive Dynamical Systems in Discrete Time, De Gruyter, Berlin, 2015. · <a href="/1326.37003" class="nowrap">Zbl 1326.37003</a></td> </tr><tr> <td>[47]</td> <td class="space">Ljung, L., Chen, T., and Mu, B., A shift in paradigm for system identification, Internat. J. Control, 93 (2020), pp. 173-180, doi:10.1080/00207179.2019.1578407. · <a href="/1453.93066" class="nowrap">Zbl 1453.93066</a></td> </tr><tr> <td>[48]</td> <td class="space">Luenberger, D G., Introduction to Dynamic Systems; Theory, Models, and Applications, Wiley, Hoboken, NJ, 1979. · <a href="/0458.93001" class="nowrap">Zbl 0458.93001</a></td> </tr><tr> <td>[49]</td> <td class="space">Marconato, A., Schoukens, M., and Schoukens, J., Filter-based regularisation for impulse response modelling, IET Control Theory Appl., 11 (2016), pp. 194-204, doi:10.1049/iet-cta.2016.0908.</td> </tr><tr> <td>[50]</td> <td class="space">Oghbaee, A., Shafai, B., and Nazari, S., Complete characterisation of disturbance estimation and fault detection for positive systems, IET Control Theory Appl., 12 (2018), pp. 883-891, doi:10.1049/iet-cta.2017.0911.</td> </tr><tr> <td>[51]</td> <td class="space">Peypouquet, J., Convex Optimization in Normed Spaces: Theory, Methods and Examples, Springer, Cham, 2015. · <a href="/1322.90004" class="nowrap">Zbl 1322.90004</a></td> </tr><tr> <td>[52]</td> <td class="space">Pillonetto, G. and De Nicolao, G., A new kernel-based approach for linear system identification, Automatica, 46 (2010), pp. 81-93, doi:10.1016/j.automatica.2009.10.031. · <a href="/1214.93116" class="nowrap">Zbl 1214.93116</a></td> </tr><tr> <td>[53]</td> <td class="space">Pillonetto, G., Dinuzzo, F., Chen, T., De Nicolao, G., and Ljung, L., Kernel methods in system identification, machine learning and function estimation: A survey, Automatica, 50 (2014), pp. 657-682, doi:10.1016/j.automatica.2014.01.001. · <a href="/1298.93342" class="nowrap">Zbl 1298.93342</a></td> </tr><tr> <td>[54]</td> <td class="space">Rantzer, A. and Valcher, M. E., A tutorial on positive systems and large scale control, in 2018 IEEE Conference on Decision and Control, , IEEE, 2018, pp. 3686-3697.</td> </tr><tr> <td>[55]</td> <td class="space">Rantzer, A. and Valcher, M. E., Scalable control of positive systems, Annu. Rev. Control. Robotics Auton. Syst., 4 (2021), pp. 319-341, doi:10.1146/annurev-control-061520-010621.</td> </tr><tr> <td>[56]</td> <td class="space">Reis, T. and Virnik, E., Positivity preserving balanced truncation for descriptor systems, SIAM J. Control Optim., 48 (2009), pp. 2600-2619, doi:10.1137/080734200. · <a href="/1203.93042" class="nowrap">Zbl 1203.93042</a></td> </tr><tr> <td>[57]</td> <td class="space">Risuleo, R. S., Bottegal, G., and Hjalmarsson, H., A nonparametric kernel-based approach to Hammerstein system identification, Automatica, 85 (2017), pp. 234-247, doi:10.1016/j.automatica.2017.07.055. · <a href="/1375.93133" class="nowrap">Zbl 1375.93133</a></td> </tr><tr> <td>[58]</td> <td class="space">Risuleo, R. S., Lindsten, F., and Hjalmarsson, H., Bayesian nonparametric identification of Wiener systems, Automatica, 108 (2019), 108480, doi:10.1016/j.automatica.2019.06.032. · <a href="/1536.93952" class="nowrap">Zbl 1536.93952</a></td> </tr><tr> <td>[59]</td> <td class="space">Roszak, B. and Davison, E. J., Necessary and sufficient conditions for stabilizability of positive LTI systems, Syst. Control Lett., 58 (2009), pp. 474-481, doi:10.1016/j.sysconle.2009.02.003. · <a href="/1166.93019" class="nowrap">Zbl 1166.93019</a></td> </tr><tr> <td>[60]</td> <td class="space">Schölkopf, B., Herbrich, R., and Smola, A. J., A generalized representer theorem, in International Conference on Computational Learning Theory, , , Springer, Cham, 2001, pp. 416-426. · <a href="/0992.68088" class="nowrap">Zbl 0992.68088</a></td> </tr><tr> <td>[61]</td> <td class="space">Shafai, B., Chen, J., and Kothandaraman, M., Explicit formulas for stability radii of nonnegative and Metzlerian matrices, IEEE Trans. Automat. Control, 42 (1997), pp. 265-270, doi:10.1109/9.554408. · <a href="/0866.93076" class="nowrap">Zbl 0866.93076</a></td> </tr><tr> <td>[62]</td> <td class="space">Shorten, R., Wirth, F., and Leith, D., A positive systems model of TCP-like congestion control: Asymptotic results, IEEE/ACM Trans. Network., 14 (2006), pp. 616-629, doi:10.1109/TNET.2006.876178.</td> </tr><tr> <td>[63]</td> <td class="space">Srinivas, N., Krause, A., Kakade, S. M., and Seeger, M. W., Information-theoretic regret bounds for Gaussian process optimization in the bandit setting, IEEE Trans. Inform. Theory, 58 (2012), pp. 3250-3265, doi:10.1109/TIT.2011.2182033. · <a href="/1365.94131" class="nowrap">Zbl 1365.94131</a></td> </tr><tr> <td>[64]</td> <td class="space">Umenberger, J. and Manchester, I. R., Scalable identification of stable positive systems, in 2016 IEEE 55th Conference on Decision and Control, , IEEE, 2016, pp. 4630-4635, doi:10.1109/CDC.2016.7798974.</td> </tr><tr> <td>[65]</td> <td class="space">Valcher, M. E., Reachability properties of continuous-time positive systems, IEEE Trans. Automat. Control, 54 (2009), pp. 1586-1590, doi:10.1109/TAC.2009.2015556. · <a href="/1367.93065" class="nowrap">Zbl 1367.93065</a></td> </tr><tr> <td>[66]</td> <td class="space">Wahba, G., Spline Models for Observational Data, SIAM, Philadelphia, 1990. · <a href="/0813.62001" class="nowrap">Zbl 0813.62001</a></td> </tr><tr> <td>[67]</td> <td class="space">Xiong, D., Chai, L., and Zhang, J., Sparse system identification in pairs of pulse and Takenaka-Malmquist bases, SIAM J. Control Optim., 58 (2020), pp. 965-985, doi:10.1137/18M1217474. · <a href="/1440.93059" class="nowrap">Zbl 1440.93059</a></td> </tr><tr> <td>[68]</td> <td class="space">Zeinaly, Y., van Schuppen, J. H., and Schutter, B. D., Linear positive systems may have a reachable subset from the origin that is either polyhedral or nonpolyhedral, SIAM J. Matrix Anal. Appl., 41 (2020), pp. 279-307, doi:10.1137/19M1268161. · <a href="/1436.93066" class="nowrap">Zbl 1436.93066</a></td> </tr><tr> <td>[69]</td> <td class="space">Zheng, M. and Ohta, Y., Positive FIR system identification using maximum entropy prior, IFAC-PapersOnLine, 51 (2018), pp. 7-12, doi:10.1016/j.ifacol.2018.09.082.</td> </tr><tr> <td>[70]</td> <td class="space">Zheng, M. and Ohta, Y., Bayesian positive system identification: Truncated Gaussian prior and hyperparameter estimation, Systems Control Letters, 148 (2021), 104857, doi:10.1016/j.sysconle.2020.104857. · <a href="/1478.93132" class="nowrap">Zbl 1478.93132</a></td> </tr><tr> <td>[71]</td> <td class="space">Zorzi, M., A second-order generalization of TC and DC kernels, IEEE Trans. Automat. Control, 69 (2024), pp. 3835-3848, doi:10.1109/TAC.2023.3337056. · <a href="/1546.93750" class="nowrap">Zbl 1546.93750</a></td> </tr><tr> <td>[72]</td> <td class="space">Zorzi, M. and Chiuso, A., The harmonic analysis of kernel functions, Automatica, 94 (2018), pp. 125-137, doi:10.1016/j.automatica.2018.04.015. · <a href="/1400.93321" class="nowrap">Zbl 1400.93321</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. 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