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.
This paper studies the robust stabilization for a class of nonlinear time-delay fractional order (FO) systems in the presence of some practical aspects. The considered aspects in the FO system include: nonlinear Lipschitz functions; time-varying norm-bounded uncertain terms; and time-delays in the state variables. A major challenge in the control of time-delay systems is that the value of delay is usually not perfectly known or it may be even time-varying. In this paper, a novel asymptotic stabilizing control law is proposed which is delay independent and also has a robust manner in the presence of uncertain terms in the model which may be due to model uncertainties (parameter uncertainties or model simplification) and/or external disturbances. The proposed controller is a FO sliding mode controller that is designed such that the closed-loop system is asymptotically delay-independent stable. For this purpose, a FO sliding manifold is introduced and the occurrence of the reaching phase in a finite time is proved. Finally, in order to validate the theoretical results, an example is given and simulation results confirm the appropriate performance of the proposed controller.
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