Global Regulation by Integral Feedback for Lower-Triangular Nonlinear Systems with Actuator Failures and Limited Delays

Abstract

This paper studies the global asymptotic regulation problem for a class of lower-triangular nonlinear systems with actuator failures and limited delays. New integral controllers consisting of an integral dynamic are constructed to make all system states bounded and asymptotically convergent to zero. First, an integral dynamic is constructed and a novel state transformation is introduced, which ensures that the involved systems with actuator failures are converted into a class of auxiliary nonlinear systems without actuator failures. Second, by introducing the static high-gain technique, the problem of designing integral controllers for auxiliary nonlinear systems is converted into that of designing the gain parameter and determining the limit of the actuator delay. At last, with the help of the Lyapunov stability theorem, the gain parameter and the limit of the actuator delay are determined, and the stabilization of the auxiliary nonlinear systems yields the global asymptotic regulation of the involved systems. A physical system example is given to demonstrate the effectiveness of the proposed integral controllers.