Observer-based control for nonlinear parameter-varying systems: A sum-of-squares approach

This paper investigates the design problem of nonlinear and time-varying observer-based controllers for nonlinear parameter-varying systems without/with input constraints. With the aid of Lyapunov stability theory, the state-and-parameter-dependent linear matrix inequality conditions are obtained. These conditions are developed as convex programming problems. And a feasible solution can be obtained via sum-of-squares techniques. Thus, the commonly used backstepping/iterative methods are avoided. In addition, the effect of the bilinear product forms for the controller gain matrix and the Lyapunov functional are eliminated. A remarkable advantage of this proposed approach is that the state-and-parameter-dependent observer and the state-feedback controller can be designed independently, which significantly reduces the computational complexity. Finally, the feasibility and validity of the proposed method can be illustrated by simulation results.