H∞ control for a class of nonlinear system based on L2 gain computation

This paper addresses the state feedback H_∞ control for a class of nonlinear system based on its L₂ gain computation, where the technique of the sum of squares decomposition is applied. By reformulating the Hamilton-Jacobin inequality as a linear semi-definite optimization problem, the L₂ gain of the considered nonlinear systems can be estimated with the help of the software SOSTOOLS [1] under the sum of squares framework. A new iterative state feedback H_∞ control synthesis algorithm for the considered nonlinear system is proposed, where a state feedback H_∞ controller is synthesized iteratively based on an initial controller that can stabilize the system to a finite L₂ gain. Some examples are shown to illustrate the effectiveness of the proposed algorithm. The iterative algorithm is extended for the output feedback synthesis at the end of this paper.