Observer-Based Dissipative ISMC for Asynchronous Switched Systems: A Novel LMI Technique

This work reports design problem of the observer-based integral sliding mode control for switched time-delay systems via asynchronous switching and dissipative condition. The main purpose of observer is to estimate the system’s entire state information based on measurement outputs, and further the observer states are used to create the controller. First, an improved free-weighting matrix inequality is introduced for concerning switched systems (SSs) to reduce conservatism of the integral terms. Then, a novel asymmetric Lyapunov–Krasovskii functional (LKF) is constructed for analysing the exponential stability of SSs with time-delay. With the help of improved integral inequality and novel LKF, a new set of sufficient conditions is developed in the form of linear matrix inequalities (LMIs). The developed criteria based on the sliding mode controller with observer scheme ensure that the proposed systems is exponentially stable with dissipative performance. Finally, numerical simulations are given to illustrate the usefulness and benefit of the proposed methods.