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

Abstract

The 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 parameterindependent 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.

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