ℋ<inf>∞</inf> state-feedback control of linear systems with time-varying input delays

Abstract

In this paper, we will address the state-feedback control synthesis problem for linear systems with time-varying input delays under the integral quadratic constraint (IQC) framework. A new exact-memory control scheme is first proposed, which consists of a standard linear state-feedback control law and an internal delay loop. The delay loop is embedded in the controller structure so as to reproduce the input delay behavior of the plant. With this controller structure, the resulting delay control synthesis problem is fully characterized by a set of linear matrix inequalities (LMIs), which are convex on all design variables including the scaling factors associated with the IQC multipliers. The corresponding results on memoryless state-feedback control are also derived for cases when input-delay information is not available for feedback control. A numerical example has been used to illustrate the effectiveness of the proposed approach.