Robust H∞ Control for linear systems with delay in state or input

A Piecewise analysis method technique is proposed to investigate the H∞ control of uncertain systems with time delay in state or input. Firstly, the variation interval of the time-varying delay is divided into several subintervals with equal length. By checking the variation of derivative of the Lyapunov functional in every subinterval, some new criteria on H∞ performance analysis of the systems are derived in terms of the convexity properties of a matrix inequality and some other new analysis techniques. Then, criteria for the H∞ control design are presented, which are concluded from the H∞ performance analysis results. As applications of the derived results, H∞ performance analysis and H∞ control design are carried out for some systems, including a numerical systems and linearized truck trailer system. Discussions show that, the proposed method is effective for these systems and appears much less conservativeness than those given in the existing references.