Exponential stability of time-delay adaptive switched systems with two nonlinear disturbance

This paper investigates the exponential stability of adaptive switched systems with nonlinear perturbations and uncertain parameters. Firstly, the adaptive controller is designed for the subsystem, and in order to better apply to the real world, the free parameter matrix is introduced by constructing (L-K functional) considering that the state contains time delay and there are two nonlinear perturbations. Then an adaptive law which depends on switched signal is designed to avoid the coupling problem between the sub-adaptive laws caused by the shared state. The multi-Lyapunov function method is used to design the controller of the system. The purpose of using the switched rate is to ensure the exponential stability of the closed-loop system. The switched rule is obtained by means of the average residence time method. Combined with linear matrix inequality, The paper establishes the conditions for ensuring exponential stability of the system and conducts numerical calculations through the Matlab simulation. Furthermore, a practical example is provided to demonstrate the effectiveness of the results obtained using the controller, applicable law, and switching rate discussed in the paper.