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New results on delay-dependent dissipative control of linear systems with time delay

Xiaoxiao Lv, Xiaodi Li


In this paper, the problem of delay-dependent dissipativity is investigated for linear time-delay system in which the external input appears on output term. We develop the design methods of dissipative static state feedback such that the closed-loop system is strictly (Q, S,R)-γ-dissipative. By constructing a set of appropriated Lyapunov-Krasovskii functionals and employing Newton-Leibniz formulation and free weighting matrix method, some
(Q, S,R)-γ-dissipativity criteria and sufficient conditions for the existence of the quadratic dissipative controller are obtained in terms of linear matrix inequalities (LMIs), which can be easily verified via the Matlab LMI toolbox. The results developed in this paper are less conservative and more general than some recent work in the literature, which are illustrated by two numerical examples.


linear systems, dissipative control, Lyapunov-Krasovkii functional, linear matrix inequality (LMI), time delay.

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