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∞ 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.

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This paper considers the finite-time output feedback controller design for nonlinear discrete-time systems with time-delay and time-varying exogenous disturbances. The exogenous disturbances are unknown bounded signals. In this regard, a theorem is given and the sufficient conditions are extracted which guarantees the finite-time boundedness of the time-delay closed-loop system via selecting the appropriate Lyapunov-Krasovskii functional. Furthermore, the gain of output feedback is achieved through the feasibility testing of the derived linear matrix inequalities (LMIs). Finally, a numerical example is given to verify the effectiveness of the developed technique.

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