Finite‐dimensional characterizations of H∞ control for linear systems with delays in input and output

Abstract

AbstractWe formulate H∞ control problems for linear systems with delays in input and output, and discuss possibility of finite‐dimensional characterizations of solutions. In the case when delay exists in control input and controlled output, first, we derive an output feedback H∞ control formula of the central solution type, which is given by using solutions of finite‐ and infinite‐dimensional Riccati matrix inequalities. Second, we show that, if the controlled output is chosen such that it satisfies the ‘prediction condition’, the solution to the infinite‐dimensional Riccati inequality can be calculated by solving a finite‐dimensional Riccati inequality. We provide a system theoretic interpretation for the prediction condition, and show that, if the prediction condition is satisfied, there is an equivalent H∞ control problem for finite‐dimensional linear systems with no delay. Finally, the equivalence result is extended to the case when delay exists also in measurement output. Copyright © 2003 John Wiley & Sons, Ltd.