Observer-based H∞ finite-time controller for time-delay nonlinear one-sided Lipschitz systems with exogenous disturbances

This paper is concerned with a robust observer-based control of nonlinear one-sided Lipschitz systems in the presence of time delay, model uncertainties, and unknown energy-bounded exogenous disturbances. In this regard, firstly, an appropriate observer is designed and then a controller is achieved based on estimated state variables. Considering dynamical equations of the system together with dynamical equations of the observer error, the sufficient conditions are given for robust finite-time boundedness of the closed-loop system and satisfying the H infinity performance index. In this regard, a theorem is given and the sufficient conditions are derived in terms of feasibility testing of given linear matrix inequalities by selecting an appropriate Lyapunov-Krasovskii functional. Finally, computer simulations are performed for two examples to show the efficiency and applicability of the proposed controller.