Abstract
This paper is concerned with the stochasticH∞state feedback control problem for a class of discrete-time singular systems with state and disturbance dependent noise. Two stochastic bounded real lemmas (SBRLs) are proposed via strict linear matrix inequalities (LMIs). Based on the obtained SBRLs, a state feedbackH∞controller is presented, which not only guarantees the resulting closed-loop system to be mean square admissible but also satisfies a prescribedH∞performance level. A numerical example is finally given to illustrate the effectiveness of the proposed theoretical results.
Highlights
Because of extensive applications in economy, mechanical systems, systems with human operators, and so on, a great deal of attention has been paid to a class of stochastic linear systems governed by Ito’s stochastic differential equations over the past years [1,2,3,4]
It is noted that the study on the control of deterministic or Markov jump singular systems has made fruitful achievement on stability [14, 15], stabilization [16, 17], H∞ control [18,19,20,21,22,23,24,25], and H2/H∞ control [26], as well as sliding mode control [27, 28]
Based on the assumption proposed by [34], the problem of robust finite-time H∞ control for a class of singular stochastic systems with parametric uncertainties was further discussed in [35], and the state feedback controller ensuring that the closed-loop system was robust stochastically bounded with a prescribed H∞ performance level was designed by means of the linear matrix inequalities (LMIs)
Summary
Because of extensive applications in economy, mechanical systems, systems with human operators, and so on, a great deal of attention has been paid to a class of stochastic linear systems governed by Ito’s stochastic differential equations over the past years [1,2,3,4]. The assumption condition was reduced to rank(E, A0) = rank(E) in [36,37,38], and sufficient conditions for the mean square admissibility of stochastic singular systems were proposed in terms of strict LMIs. the state feedback H∞ control for continuous-time singular stochastic systems was investigated in [39]. In this paper, motivated by [37], we investigate stochastic H∞ state feedback control problem for discrete-time singular systems with state and disturbance dependent noise. (ii) The suitable LMI conditions are presented, which meet the requirement of the mean square admissibility for the singular stochastic system and ensure the irrelevance of the state x(k) and the sequence of the random variables {w(k)}k≥0, while the above irrelevance is crucial to discuss the control problem of discrete-time stochastic systems.
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