A Convex Approach to State Feedback Synthesis for Polynomial Nonlinear Systems with Input Saturation

摘要

Ignoring input limitation in control systems often causes closed-loop instability or performance degradation. This paper proposes a sum of squares approach to a problem of state feedback controller synthesis for polynomial nonlinear systems with input saturation. A polytope representation of the saturation function gives tractable sufficient stability conditions for the problem. The design procedure follows two steps which are not iterative. In the first step, the matrix sum of squares relaxation is directory applied to the problem. In the second step, the annihilator of polynomials decreases the conservativeness of the first design to expand an estimate of the domain of attraction of the equilibrium point of the closed-loop system. The result is an extension of a linear matrix inequality approach, which has been developed for linear systems with input saturation, to polynomial nonlinear systems. Numerical examples illustrate the proposed design procedure.