State Feedback Synthesis for Polynomial Systems with Input Saturation using Convex Optimization

This paper proposes a convex optimization approach to state feedback synthesis for input-afflne polynomial systems with input saturation. A polytope model of the saturation is introduced to the system analysis, and leads a sufficient condition of the state feedback design as a convex problem from a viewpoint of robust control. The result is an extension of a linear matrix inequality approach for linear systems with input saturation. A redesign method is also proposed in which polynomial annihilators decrease the conservativeness of the first design. Both the design procedures can be computed by using matrix sum of squares relaxations and semidefinite programming. The proposed approach does not take any iterative strategies, but could take two steps of convex optimization to expand the invariant set.