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

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.