Delay‐dependent robust H_∞ control for uncertain singular time‐delay system with Markovian jumping parameters

Abstract

SUMMARYThe problem of robust H ∞ control for a class of uncertain singular time‐delay systems with Markovian jumping parameters is addressed in this paper. The considered Markovian jump singular systems involve constant time delay and norm‐bounded uncertainties. On the basis of LMI approach, a delay‐dependent condition is proposed, which ensures the nominal Markovian jump singular system to be regular, impulse‐free and stochastically stable. From the delay‐dependent condition, a sufficient condition leading to the existence of a state feedback controller that guarantees the robust admissibility and the H ∞ performance is also given. A numerical example is given to demonstrate the applicability of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.

Stochastic Stability Criteria for Neutral Distributed Parameter Systems with Markovian Jump

“…For less conservative results, the delay-dependent stability has been discussed in [17][18][19][20]. Other control methods have also been extensively and thoroughly studied such as robust delay-dependent H ∞ control [21,22], nonfragile control [23][24][25], sliding mode control [26,27], H ∞ sliding mode control [28], and the references therein. e transition rates in many references mentioned above have been supposed to be completely known.…”

Delay-Dependent Finite-TimeH∞Controller Design for a Kind of Nonlinear Descriptor Systems via a T-S Fuzzy Model

“…However, it is noteworthy that singular systems not only describe actual physical systems better but also are also more widely utilized than ordinary ones. So in the past decades, descriptor systems have attracted much attention [7,17,19,[25][26][27][28][29][30].…”

“…On the other hand, the problem of ∞ control has been a topic of growing interestover the past decades. A great number of results on ∞ control for the state-space and descriptor systems have been reported in literatures [29,[31][32][33][34][35]. However, the related research on finite-time ∞ control of fuzzy descriptor systems is relatively less.…”

Finite-time H<inf>&#x221E;</inf> performance analysis for a kind of T-S fuzzy descriptor system with time-delay

“…So there has been an increasing interest in the stability analysis and stabilization for time delay systems in the last decades [9][10][11][12][13][14][15][16]. Delay-dependent discussions which take into account the size of delays, are of less conservative, especially in the case of small time delays [13].…”

“…On the other hand, the problem of H control has been a topic of growing interest over the past decades. Some results on H control This work is supported by National Nature Science Foundation under Grant 61273003, 61273308, 61273011 for the state-space and descriptor systems have been reported in literatures [6][7][8][9][10]14].…”