Robust H∞ controller synthesis for uncertain systems with multiple time-varying delays: An LMI approach

Abstract This paper is concerned with the robust H ∞ control problem for linear uncertain systems with multiple time-varying delays. Based on the linear matrix inequality (LMI) approach, we develop a method for synthesizing a robust H ∞ dynamic output feedback control law which guarantees the quadratic stability of the closed-loop system and reduces, to a prescribed level, the effect of the disturbance input on the controlled output. A sufficient condition for the existence of a robust H ∞ controller of any order is proposed in terms of three LMIs. One can easily design a robust H ∞ controller by solving the three LMIs numerically very efficiently via convex and quasi-convex optimization techniques.

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