Adaptive state feedback control for nonlinear systems with multiple interval time-varying delays and non-symmetric dead-zone input: A Lyapunov-Krasovskii approach

This paper addresses the stability analysis and adaptive state feedback control for a class of nonlinear discrete-time systems with multiple interval time-varying delays and non-symmetric dead-zone input. The multiple interval time-varying delays uncertainties are bounded by the nonlinear function with unknown coefficients. The non-symmetric dead-zone input without the knowledge of the dead-zone parameters is considered for the nonlinear system. The smooth adaptive state feedback controller is designed. By introducing the new Lyapunov-Krasovskii functional, it can be seen that the solutions of the closed-loop error system converge to an adjustable bounded region. In general, the proposed adaptive state feedback control strategy does not require the knowledge of maximum and minimum values for the characteristic slopes, and the knowledge of all system states. The control design conditions are relaxed because the system output is available for the controller design. Finally, three simulation examples are performed to show the effectiveness of the proposed methods.