A nonlinear static output controller design for polynomial systems: An iterative sums of squares approach

This paper presents an iterative sum of squares approach for designing a nonlinear static output feedback control for polynomial systems. In this work, the problem of designing a nonlinear static output feedback controller is converted into solvability conditions of polynomial matrix inequalities. An iterative algorithm based on the sum of squares decomposition technique is proposed to resolve the non-convex terms issue and convert it to the convex problem, hence a feasible solution for polynomial matrix inequalities can be obtained efficiently. Numerical examples are provided at the end of the paper as to demonstrate the validity of applied method.