Nonlinear H∞ control using sum of squares decomposition

This paper discusses the state feedback H
_∞
control for a class of nonlinear system based on its L
₂
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 L
₂
gain of the considered nonlinear systems can be computed with the aid 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 L
₂
gain. Some examples are shown to illustrate the effectiveness of the proposed algorithm.