Setpoint Tracking for a Class of Lur’e Discrete-Time Systems
Résumé
Setpoint tracking for a class of discrete-time nonlinear plants is addressed. The plant under consideration is a feedback interconnection of a square linear system (with the same number of inputs and outputs) and a nonlinearity obeying to an incremental quadratic constraint. Within this setting, we design a dynamic feedback controller ensuring, for the closed-loop system, internal exponential stability and output tracking of constant setpoints with tunable performance guarantees. A proportional-integral feedback controller is proposed. Combining Lyapunov theory and the use of a quadratic Lyapunov function, sufficient conditions for the design of the controller are stated in terms of linear matrix inequalities. An optimal controller design algorithm based on semidefinite programming is proposed to design the controller gains to improve transient performance and limit the control effort. Two numerical examples illustrate the application of the proposed methodology.
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