Shao, Hanyong; Lam, James; Feng, Zhiguang Sampling-interval-dependent stability for linear sampled-data systems with non-uniform sampling. (English) Zbl 1347.93170 Int. J. Syst. Sci., Princ. Appl. Syst. Integr. 47, No. 12, 2893-2900 (2016). Summary: This paper is concerned with the sampling-interval-dependent stability of linear sampled-data systems with non-uniform sampling. A new Lyapunov-like functional is constructed to derive sampling-interval-dependent stability results. The Lyapunov-like functional has three features. First, it depends on time explicitly. Second, it may be discontinuous at the sampling instants. Third, it is not required to be positive definite between sampling instants. Moreover, the new Lyapunov-like functional can make use of the information fully of the sampled-data system, including that of both ends of the sampling interval. By making a new proposition for the Lyapunov-like functional, a sampling-interval-dependent stability criterion with reduced conservatism is derived. The new sampling-interval-dependent stability criterion is further extended to linear sampled-data systems with polytopic uncertainties. Finally, examples are given to illustrate the reduced conservatism of the stability criteria. Cited in 5 Documents MSC: 93C57 Sampled-data control/observation systems 93C05 Linear systems in control theory 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory 93C15 Control/observation systems governed by ordinary differential equations 93C41 Control/observation systems with incomplete information Keywords:Lyapunov-like functional; sampled-data systems; sampling-interval-dependent stability PDF BibTeX XML Cite \textit{H. Shao} et al., Int. J. Syst. Sci., Princ. Appl. Syst. Integr. 47, No. 12, 2893--2900 (2016; Zbl 1347.93170) Full Text: DOI References: [1] DOI: 10.1007/978-1-4471-3037-6 · doi:10.1007/978-1-4471-3037-6 [2] DOI: 10.1016/j.automatica.2009.11.017 · Zbl 1205.93099 · doi:10.1016/j.automatica.2009.11.017 [3] DOI: 10.1016/j.automatica.2004.03.003 · Zbl 1072.93018 · doi:10.1016/j.automatica.2004.03.003 [4] DOI: 10.1016/j.automatica.2008.10.017 · Zbl 1168.93373 · doi:10.1016/j.automatica.2008.10.017 [5] DOI: 10.1109/TSMCB.2003.808181 · doi:10.1109/TSMCB.2003.808181 [6] DOI: 10.1049/iet-cta.2010.0700 · doi:10.1049/iet-cta.2010.0700 [7] DOI: 10.1109/TAC.2008.919547 · Zbl 1367.93179 · doi:10.1109/TAC.2008.919547 [8] DOI: 10.1080/00207721.2012.687785 · Zbl 1307.93246 · doi:10.1080/00207721.2012.687785 [9] DOI: 10.1002/rnc.1704 · Zbl 1261.93071 · doi:10.1002/rnc.1704 [10] DOI: 10.1016/j.automatica.2011.09.029 · Zbl 1244.93094 · doi:10.1016/j.automatica.2011.09.029 [11] DOI: 10.1080/00207721.2010.550401 · Zbl 1307.93244 · doi:10.1080/00207721.2010.550401 [12] DOI: 10.1016/j.sysconle.2007.10.009 · Zbl 1140.93036 · doi:10.1016/j.sysconle.2007.10.009 [13] DOI: 10.1016/j.automatica.2010.05.006 · Zbl 1205.93100 · doi:10.1016/j.automatica.2010.05.006 [14] DOI: 10.1016/j.automatica.2011.09.033 · Zbl 1244.93095 · doi:10.1016/j.automatica.2011.09.033 [15] DOI: 10.1016/j.automatica.2008.09.010 · Zbl 1168.93387 · doi:10.1016/j.automatica.2008.09.010 [16] DOI: 10.1016/j.automatica.2008.10.002 · Zbl 1153.93450 · doi:10.1016/j.automatica.2008.10.002 [17] DOI: 10.1080/00207721.2012.659704 · Zbl 1278.93160 · doi:10.1080/00207721.2012.659704 [18] DOI: 10.1109/TAC.2006.886495 · Zbl 1366.93451 · doi:10.1109/TAC.2006.886495 [19] Yue D., IEEE Transactions on Automatic Control 51 pp 640– (2004) [20] DOI: 10.1016/j.jfranklin.2014.05.014 · Zbl 1395.93362 · doi:10.1016/j.jfranklin.2014.05.014 [21] DOI: 10.1049/iet-cta.2012.0814 · doi:10.1049/iet-cta.2012.0814 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.