Infinite-dimensional LMI approach to H∞ control synthesis for linear systems with time delay

This paper considers a synthesis problem of H^∞ controllers for linear systems with time delay in the form of delay-dependent memory state feedback, and develops a new Linear Matrix Inequalities (LMIs) approach. First, we present an existence condition and an explicit formula of H^∞ controllers in terms of infinite-dimensional LMIs. This result is rather general in the sense that it covers, as special cases, some known results for the cases of delay-independent/dependent and memoryless/memory controllers, while the infinity dimensionality of the LMIs makes the result difficult to apply. Second, we introduce a technique to reduce the infinite-dimensional LMIs to a finite number of LMIs, and present a feasible algorithm for synthesis of H^∞ controllers based on the finite-dimensional LMIs.