On finite time stability with guaranteed cost control of uncertain linear systems

summary:This paper deals with the design of a robust state feedback control law for a class of uncertain linear time varying systems. Uncertainties are assumed to be time varying, in one-block norm bounded form. The proposed state feedback control law guarantees finite time stability and satisfies a given bound for an integral quadratic cost function. The contribution of this paper is to provide a sufficient condition in terms of differential linear matrix inequalities for the existence and the construction of the proposed robust control law. In particular, the construction of the feedback control law is brought back to a feasibility problem which can be solved inside the convex optimization framework. The effectiveness of the proposed approach is shown by means of the results obtained on a numerical and a physical example

A new LMI-based robust finite-time sliding mode control strategy for a class of uncertain nonlinear systems

summary:This paper presents a novel sliding mode controller for a class of uncertain nonlinear systems. Based on Lyapunov stability theorem and linear matrix inequality technique, a sufficient condition is derived to guarantee the global asymptotical stability of the error dynamics and a linear sliding surface is existed depending on state errors. A new reaching control law is designed to satisfy the presence of the sliding mode around the linear surface in the finite time, and its parameters are obtained in the form of LMI. This proposed method is utilized to achieve a controller capable of drawing the states onto the switching surface and sustain the switching motion. The advantage of the suggested technique is that the control scheme is independent of the order of systems model and then, it is fairly simple. Therefore, there is no complexity in the utilization of this scheme. Simulation results are provided to illustrate the effectiveness of the proposed scheme