Robust variance-constrained H_∞ control for stochastic systems with multiplicative noises

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• 作者：Zidong Wang ; Fuwen Yang ; Daniel W.C. Ho ; Xiaohui Liu
• 关键词：Stability ; ; none ; color ; black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6WK2-4K7WTYK-8&_mathId=mml6&_user=10&_cdi=6894&_rdoc=39&_acct=C000050221&_version=1&_userid=10&md5=ed8b4ed71d947d76e5378cb171616ad
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2007
• 出版时间：1 April 2007
• 年：2007
• 卷：328
• 期：1
• 页码：487-502
• 全文大小：167 K

文摘

In this paper, the robust variance-constrained H_∞ control problem is considered for uncertain stochastic systems with multiplicative noises. The norm-bounded parametric uncertainties enter into both the system and output matrices. The purpose of the problem is to design a state feedback controller such that, for all admissible parameter uncertainties, (1) the closed-loop system is exponentially mean-square quadratically stable; (2) the individual steady-state variance satisfies given upper bound constraints; and (3) the prescribed noise attenuation level is guaranteed in an H_∞ sense with respect to the additive noise disturbances. A general framework is established to solve the addressed multiobjective problem by using a linear matrix inequality (LMI) approach, where the required stability, the H_∞ characterization and variance constraints are all easily enforced. Within such a framework, two additional optimization problems are formulated: one is to optimize the H_∞ performance, and the other is to minimize the weighted sum of the system state variances. A numerical example is provided to illustrate the effectiveness of the proposed design algorithm.