Observer-Based Mixed H2/H∞ Control Design for Linear Systems with Time-Varying Delays: An LMI Approach

This paper presents a convex optimization method for observer-based mixed H2/H∞ control design of linear systems with time-varying state, input and output delays. Delay- dependent sufficient conditions for the design of a desired observer-based control are given in terms of linear matrix inequalities (LMIs). An observer-based controller which guarantees asymptotic stability and a mixed H2/H∞ performance for the closed-loop system of the linear system with time-varying delays is then developed. A Lyapunov-Krasovskii method underlies the observer-based mixed H2/H∞ control design. A numerical example with simulation results illustrates the effectiveness of the methodology.

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