Full InformationH∞-Control for Discrete-Time Infinite Markov Jump Parameter Systems

Abstract

In this paper we consider the full information discrete-time H -control problem ϱ for the class of linear systems with Markovian jumping parameters. The state-space of the Markov chain is assumed to take values in a countably infinite set. Full information here means that the controller has access to both the state-variables and jump-variables. A necessary and sufficient condition for the existence of a feedback controller that makes the l l -induced norm of the system less than a 2 prespecified bound is obtained. This condition is written in terms of a set of infinite coupled algebraic Riccati equations.

Mode-Independent H∞ Control of Discrete-Time Markovian Jump Linear Systems

“…This is in contrast with existing approaches of H ∞ control of MJL systems, such as those of Costa and do Val (1996), Fragoso et al (1995), and Shi et al (1999), which require the jumping parameter to be accessible.…”

“…Note that in this situation, Theorem 2 provides necessary and sufficient conditions for the solution of this H ∞ control problem and this theorem is equivalent to the main result of Costa and do Val (1996), when restricted to the case where the Markov chain takes value in a finite set. 2…”

“…(Costa and do Val, 1996) Given the system (S 1 ) and a scalar γ > 0, the following conditions are equivalent:…”

“…This class of systems is very appropriate to model plants whose structure is subject to random abrupt changes due to, for instance, random component failures, abrupt environment disturbance, changes of the operating point of a linearized model of a nonlinear system, etc. A number of control problems related to discretetime MJL systems has been analysed by several authors; see, for instance, Blair and Sworder (1975), Boukas and Liu (2001), Costa and do Val (1996), Costa and Fragoso (1993), Costa and Marques (2000), Fragoso (1989), Fragoso et al (1995), Ji and Chizeck (1990), Ji et al (1991), Morozan (1983), Shi et al (1999), Wonham (1970) and the references therein. In particular with regard to H ∞ control of discrete-time MJL systems, state-feedback control have been studied in, for instance, Costa and do Val (1996) and Fragoso et al (1995), whereas robust H ∞ control schemes have been proposed in, e.g.…”

Robust stabilisation control for discrete-time networked control systems

“…Stability analysis of NCSs is investigated in Walsh, Ye, and Bushnell (1999), Beldiman, Walsh, and Bushnell (2000), Zhang, Branicky, and Phillips (2001), Antsaklis (2003, 2004) and Zhivoglyadov and Middleton (2003), and stabilising controllers are designed in Nilsson, Bernhardsson, and Wittenmark (1998) and Zhang, Shi, Chen, and Huang (2005). In the literature, stochastic approaches are typically adopted to deal with network packet dropout and to establish the stability of the NCS in the sense of mean square statistics (Ji, Chizeck, Feng, and Loparo 1991;Costa and Fragoso 1993;Costa and do Val 1996;Xiao, Hassibi, and How 2000;Seiler and Sengupta 2005;Wu and Chen 2007). The works of Seiler and Sengupta (2005), Elia (2005), Yue, Han, and Lam (2005) and Hu and Yan (2007) adopt robust control theory for the analysis and design of NCSs.…”