Delay‐dependent H∞ control of parameter‐varying delayed systems via parameter‐dependent Lyapunov function approach

Abstract

AbstractThe H∞ control problem of parameter‐varying delayed systems is investigated in this paper. The state‐space matrices of the systems are assumed to be dependent on a vector of time‐varying real parameters which are assumed to be real‐time measurable. The delays related to the parameter‐varying systems are assumed to be unknown but with known upper bounds and to be in the states and control inputs. A delay‐dependent H∞ performance condition of the system under consideration is derived by using a new parameter‐dependent Lyapunov function. Based on the H∞ performance condition, a linear matrix inequality (LMI) based H∞ control strategy is proposed by using auxiliary variable technique. The combined parameter‐dependent and delay‐dependent results are less conservative due to the generality of the parameter‐dependent and delay‐dependent Lyapunov function used, which includes the parameter‐independent one as a special case. It is shown that the underling H∞ control problem can be solved as LMI optimization problems that can be numerically computed very efficiently. A numerical example is also given to demonstrate the applicability of the proposed approach. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society