Robust H∞ static output feedback controller design for parameter dependent polynomial systems: An iterative sums of squares approach

This paper considers the problem of designing a robust H∞ static output feedback controller for polynomial systems with parametric uncertainties. Sufficient conditions for the existence of a nonlinear H∞ static output feedback controller are given in terms of solvability conditions of polynomial matrix inequalities. An iterative sum of squares decomposition is proposed to solve these polynomial matrix inequalities. The proposed controller guarantees that the closed-loop system is stable and the L2-gain of the mapping from exogenous input noise to the controlled output is less than or equal to a prescribed value. Numerical examples are provided to demonstrate the validity of applied methods.