H∞ Dynamic output feedback control of LPV time-delay systems via dilated linear matrix inequalities

Abstract

This paper uses the linear matrix inequality dilation approach to deal with robust stability and H∞ dynamic output feedback controller synthesis for linear parameter varying delayed systems with variable delay. This approach can express the original non-convex problem in terms of convex linear matrix inequalities and consequently reduces the conservatism of linear matrix inequality synthesis without dilation. Both delay-dependent stability and H∞ performance are studied in a quadratic context. Furthermore, a Lyapunov–Krasovskii functional is used to derive a delay-dependent criterion formulated in terms of a linear matrix inequality that will be used to search for an H∞ linear parameter varying delayed dynamic output feedback controller. To achieve this aim we use an integral inequality which plays a key role in the derivation of this criterion and enables the reduction of the H∞ cost in comparison to other results.