Delay-independent sliding mode control of time-delay linear fractional order systems

Abstract

This paper considers the problem of delay-independent stabilization of linear fractional order (FO) systems with state delay. As in most practical systems in which the value of delay is not exactly known (or is time varying), a new approach is proposed in this paper, which results in asymptotic delay-independent stability of the closed-loop time-delay FO system. For this purpose, a novel FO sliding mode control law is proposed in which its main advantage is its independence to delay. Furthermore, a novel appropriate delay-independent sliding manifold is suggested. Additionally, two theorems are given and proved, which guarantee the occurrence of the reaching phase in finite time and the asymptotic delay-independent stability conditions of the dynamic equations in the sliding phase. Finally, in order to verify the theoretical results, two examples are given and simulation results confirm the performance of the proposed controller.