{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:23:14Z","timestamp":1760242994915,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2015,4,27]],"date-time":"2015-04-27T00:00:00Z","timestamp":1430092800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, the stabilization problem in switched linear systems with time-varying delay under constrained state and control is investigated. The synthesis of bounded state-feedback controllers with memory ensures that a closed-loop state is positive and stable. Firstly, synthesis with a sign-restricted (nonnegative and negative) control is considered for general switched systems; then, the stabilization issue under bounded controls including the asymmetrically bounded controls and states constraints are addressed. In addition, the results are extended to systems with interval and polytopic uncertainties. All the proposed conditions are solvable in term of linear programming. Numerical examples illustrate the applicability of the results.<\/jats:p>","DOI":"10.3390\/e17052655","type":"journal-article","created":{"date-parts":[[2015,4,27]],"date-time":"2015-04-27T12:16:51Z","timestamp":1430137011000},"page":"2655-2676","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["State Feedback with Memory for Constrained Switched Positive Linear Systems"],"prefix":"10.3390","volume":"17","author":[{"given":"Jinjin","family":"Liu","sequence":"first","affiliation":[{"name":"Key Laboratory of Measurement and Control of CSE, Ministry of Education, School of Automation, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kanjian","family":"Zhang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Measurement and Control of CSE, Ministry of Education, School of Automation, Southeast University, Nanjing 210096, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,4,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1556","DOI":"10.1109\/9.241576","article-title":"Regulator problem of linear continuous-time systems with constrained control","volume":"38","author":"Benzaouia","year":"1993","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1747","DOI":"10.1016\/S0005-1098(99)00113-2","article-title":"Set invariance in control","volume":"35","author":"Blanchini","year":"1999","journal-title":"Automatica"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Maciejowski, J.M. (2000). Predictive Control with Constraints, Prentice Hall.","DOI":"10.1049\/ic:20000115"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1016\/S0005-1098(00)00193-X","article-title":"Control of linear systems subject to input constraints: A polynomial approach","volume":"36","author":"Henrion","year":"2001","journal-title":"Automatica"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Rami, M.A., Tadeo, F., and Benzaouia, A. (2007, January 9\u201313). Control of constrained positive discrete systems. New York, NY, USA.","DOI":"10.1109\/ACC.2007.4282448"},{"key":"ref_6","first-page":"151","article-title":"Controller synthesis for positive linear systems with bounded controls","volume":"54","author":"Rami","year":"2007","journal-title":"IEEE Trans. Circuits Syst. II"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Shorten, R., and Narendra, K. (1999, January 2\u20134). Necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for two stable second order linear time-invariant systems. San Diego, CA, USA.","DOI":"10.1109\/ACC.2000.878913"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1109\/TAC.2002.806661","article-title":"A result on common quadratic Lyapunov functions","volume":"48","author":"Shorten","year":"2003","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1069","DOI":"10.1109\/5.871309","article-title":"Perspectives and results on the stability and stabilizability of hybrid systems","volume":"88","author":"Decarlo","year":"2000","journal-title":"Proc. IEEE"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1109\/81.739260","article-title":"Recent trends in the stability analysis of hybrid dynamical systems","volume":"46","author":"Michel","year":"1999","journal-title":"IEEE Trans. Circuits Syst. I"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1109\/37.793443","article-title":"Basic problems in stability and design of switched systems","volume":"19","author":"Liberzon","year":"1999","journal-title":"IEEE Control Syst. Magzine"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1109\/TAC.2008.2012009","article-title":"Stability and stabilizability of switching linear systems: A survey of recent results","volume":"54","author":"Lin","year":"2009","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Farina, L., and Rinaldi, S. (2000). Positive Linear Systems: Theory and Applications, Wiley.","DOI":"10.1002\/9781118033029"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"616","DOI":"10.1109\/TNET.2006.876178","article-title":"A positive systems model of TCP-like congestion control: asymptotic results","volume":"14","author":"Shorten","year":"2006","journal-title":"IEEE\/ACM Trans. Netw"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"988","DOI":"10.1109\/TAC.2003.812781","article-title":"Coordination of groups of mobile autonomous agents using nearest neighbour rules","volume":"48","author":"Jadbabaie","year":"2003","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1093","DOI":"10.1002\/rnc.1628","article-title":"Discrete-time control for switched positive systems with application to mitigating viral escape","volume":"21","author":"Vargas","year":"2011","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1346","DOI":"10.1109\/TAC.2007.900857","article-title":"On linear copositive Lyapunov functions and the stability of switched positive linear systems","volume":"52","author":"Mason","year":"2007","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1933","DOI":"10.1109\/TAC.2010.2049918","article-title":"Linear copositive Lyapunov functions for continuous-time positive switched systems","volume":"55","author":"Fornasini","year":"2010","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1994","DOI":"10.1080\/00207721.2012.683830","article-title":"A common linear copositive Lyapunov function for switched positive linear systems with commutable subsystems","volume":"44","author":"Tong","year":"2013","journal-title":"Int. J. Syst. Sci"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"578","DOI":"10.1002\/rnc.2777","article-title":"Stability of a class of switched positive linear time-delay systems","volume":"23","author":"Zhao","year":"2013","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1132","DOI":"10.1016\/j.automatica.2012.03.008","article-title":"Stability of switched positive linear systems with average dwell time switching","volume":"48","author":"Zhao","year":"2012","journal-title":"Automatica"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/s12555-012-0287-7","article-title":"Robust stabilization of switched positive linear systems with uncertainties","volume":"11","author":"Zhang","year":"2013","journal-title":"Int. J. Control Autom. Syst"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1208","DOI":"10.1109\/TAC.2011.2173416","article-title":"Stability and stabilizability criteria for discrete-time positive switched systems","volume":"57","author":"Fornasini","year":"2012","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/j.nahs.2013.01.001","article-title":"Stability, L1-gain and control synthesis for positive switched systems with time-varying delay","volume":"9","author":"Xiang","year":"2013","journal-title":"Nonlinear Anal. Hybrid Syst"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Zhang, J., Han, Z., and Zhu, F. (2013). L1-gain analysis and control synthesis of positive switched systems. Int. J. Syst. Sci.","DOI":"10.1080\/00207721.2013.849773"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1002\/rnc.2870","article-title":"Finite-time stability of switched positive linear systems","volume":"24","author":"Chen","year":"2014","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"ref_27","first-page":"205","article-title":"Stability and stabilization of positive systems with time varying delays","volume":"389","author":"Rami","year":"2009","journal-title":"Lect. Notes Control Inf. Sci"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1016\/j.ejcon.2013.05.001","article-title":"Estimation of linear positive systems with unknown time-varying delays","volume":"19","author":"Rami","year":"2013","journal-title":"Eur. J. Control"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1684","DOI":"10.1109\/TAC.2011.2122710","article-title":"Stability analysis of positive switched linear systems with delays","volume":"56","author":"Liu","year":"2011","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1596","DOI":"10.1109\/TAC.2009.2017961","article-title":"Constraints control of positive systems with delays","volume":"54","author":"Liu","year":"2009","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_31","first-page":"193","article-title":"Constraints control of positive discrete-time systems with delays","volume":"55","author":"Liu","year":"2008","journal-title":"IEEE Trans. Circuits Syst. II"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Hmamed, A., Benzaouia, A., Rami, M.A., and Tadeo, F. (2008, January 6\u201311). Memoryless control to drive states of delayed continuous-time systems within the nonnegative orthant. Seoul, Korea.","DOI":"10.3182\/20080706-5-KR-1001.00662"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2041","DOI":"10.1049\/iet-cta.2009.0616","article-title":"State-feedback with memory for controlled positivity with application to congestion control","volume":"4","author":"Bolajraf","year":"2010","journal-title":"IET Control Theory Appl"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"182","DOI":"10.3166\/ejc.18.182-190","article-title":"Stabilization under constrained states and controls of positive systems with time delays","volume":"18","author":"Hmamed","year":"2012","journal-title":"Eur. J. Control"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1684","DOI":"10.1109\/TAC.2011.2122710","article-title":"Stability analysis of positive switched linear systems with delays","volume":"57","author":"Liu","year":"2011","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Shen, J., and Lam, J. (2014, January 28\u201330). Constrained Control of Switched Positive Systems with Discrete and Distributed Delays. Nanjing, China.","DOI":"10.1109\/ChiCC.2014.6895974"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/5\/2655\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:45:23Z","timestamp":1760215523000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/17\/5\/2655"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,4,27]]},"references-count":36,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2015,5]]}},"alternative-id":["e17052655"],"URL":"https:\/\/doi.org\/10.3390\/e17052655","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2015,4,27]]}}}