Constrained hybrid control for parametric uncertainty systems via step-function method

In this paper, considering that sometimes signal transmission may be interrupted, or signal input errors may occur, we establish a novel class of parametric uncertainty hybrid control system models including the impulsive control signals under saturated inputs, which can reflect the signal transmission process more realistically. Based on the step-function method, improved polytopic representation approach and Schur complement, we find the stability conditions, which are less conservative than those with the traditional Lyapunov method, of the considered control system. In addition, we investigate the design of the control gains and the auxiliary control gains for easily finding the suitable control signals, the auxiliary signals and the estimation of the attraction domain. Moreover, our proposed methods are applied to the fixed time impulse problems of uncertain systems with or without Zeno behavior. Simulation results for the uncertain neural network systems are presented to show the feasibility and effectiveness of our stabilization methods using the step-function.