Finite-horizon H∞ control for a class of time-varying nonlinear systems subject to sensor and actuator saturations

In this paper, a time-varying dynamic output feedback controller is designed, which aims to solve the finite-horizon H∞ control problem for a class of discrete-time time-varying nonlinear systems subject to actuator and sensor saturations. The nonlinearities of the system under consideration satisfy the sector conditions, which include the Lipschitz non-linearities as a special case. To effectively handle the saturation nonlinearities, a compact convex hull representation is utilized, which leads to less conservative conditions for the controller design than the existing results due to imposition of extra slack variables. The sufficient conditions derived are expressed in the form of a series of recursive linear matrix inequalities. By outlining an implementation algorithm, the finite-horizon H∞ controller can be designed online. Finally, a numerical example is presented to demonstrate the feasibility and efficacy of the proposed method.