Stability and robust stabilization of 2-D continuous–discrete systems in Roesser model based on KYP lemma

Abstract

This paper investigates the problem of stability and robust stabilization of two-dimensional (2-D) continuous-discrete systems in Roesser model. Based on KalmanYakubovich-Popov (KYP) lemma, sufficient conditions of stability of the systems are proposed in terms of linear matrix inequalities (LMIs). Moreover, combining generalized KYP lemma with frequency-partitioning idea, the conservativeness of the stability conditions may be further reduced. Robust stabilization using state feedback is studied as well and stabilizing feedback gain matrices are constructed based on the solutions of certain LMIs. In addition, the stability analysis of a class of differential repetitive processes, a special case of 2-D continuous-discrete systems in Roesser model, can adopt the results in this manuscript. Numerical examples are presented to verify the effectiveness of the method.

Iterative Learning Control for Linear Differential Systems With Additional Performance Requirements

“…As discussed earlier, the representation (6) can facilitate stability analysis and control synthesis. Specifically, based on the results provided in [7], [16], [17], the process (6) is said to be stable along the trial if det(sI − A)det(zI − D 0 ) = 0, and…”

Finite-time boundedness of two-dimensional positive continuous-discrete systems in Roesser model

“…Robust stability and performance analysis of 2D mixed continuous-discrete-time systems with uncertainty were investigated in Chesi and Middleton (2016). Stability and robust stabilization of 2-D continuous-discrete systems were studied by using KYP lemma in Wang et al (2017).…”

Robust filtering for uncertain two‐dimensional continuous‐discrete state‐delay systems in finite frequency domains

“…Recently, some results have addressed this issue and generalised the standard Kalman‐Yakubivich‐Popov lemma [23] to both one‐dimensional (1D) systems and multi‐dimensional ( n ‐D) systems [9, 24–27]. Based on the generalised KYP (GKYP) lemma, which is used to directly transfer the FDI over the finite frequency range to an equivalent linear matrix inequality (LMI), many control problems in finite frequency range have been studied [7, 9, 13, 27–31].…”

“…Based on the result, delay‐dependent finite frequency bounded ream lemmas (FF BRLs) and finite frequency positive real lemmas (FF PRLs) for uncertain 2D continuous/discrete/continuous‐discrete state delay Roesser systems are proposed. Second, although some recent results for 2D continuous‐discrete Roesser systems were given in finite frequency ranges [7, 9], however, to authors' knowledge, few reports on the robust filtering problem for uncertain 2D continuous‐discrete Roesser systems with state delays in finite frequency range exist. In the paper, by the given delay‐dependent FF BRLs, sufficient conditions for the existence of filters are obtained in terms of LMIs.…”