A Novel Optimal Sliding Mode Control For Multiple Time-Delay Systems

This paper considers the problem of delay-independent optimal sliding mode control design for uncertain systems with multiple constant delays. An improved delay-independent framework for the design of SMC is established in terms of a linear matrix inequality for time-delay systems, in which multi-channel H
₂
performances of the closed-loop system are under control. Unlike most of the existing methods, the required level of control effort to maintain sliding will be taken into account in this new framework. Our two-stage SMC is constructed as follows. Firstly, a certain state feedback gain is designed while assigning some of the closed-loop eigenvalues precisely to a predetermined stable location as well as ensuring a prescribed multi-channel H
₂
performance level of the closed-loop system. In the second stage, we will find the optimal switching surface associated with the gain designed in the first stage via a novel approach developed for this goal while ensuring the stability of the reduced-order dynamics.