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

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.