Robust H∞ control for uncertain systems with heterogeneous time-varying delays via static output feedback

This paper is concerned with the problem of robust H-infinity, control for a novel class of uncertain linear continuous-time systems with heterogeneous time-varying state/input delays and norm-bounded parameter uncertainties. The objective is to design a static output feedback controller such that the closed-loop system is asymptotically stable while satisfying a prescribed H-infinity, performance level for all admissible uncertainties. By constructing an appropriate Lyapunov-Krasovskii functional, a delay-dependent stability criterion of the closed-loop system is presented with the help of the Jensen integral inequality. From the derived criterion, the solutions to the problem are formulated in terms of linear matrix inequalities and hence are tractable numerically. A simulation example is given to illustrate the effectiveness of the proposed design method.