Nonlinear robust H∞ static output feedback controller design for parameter dependent polynomial systems: An iterative sum of squares approach

The design of a robust nonlinear H_∞ static output feedback controller for parameter dependent polynomial systems is a hard problem. This paper presents a computational relaxation in form of an iterative design approach. The proposed controller guarantees the L₂-gain of the mapping from exogenous input noise to the controlled output is less than or equal to a prescribed value. The sufficient conditions for the existence of nonlinear H_∞ static output feedback controller are given in terms of solvability conditions of polynomial matrix inequalities, which are solved using sum of squares decomposition. Numerical examples are provided to demonstrate the validity of the applied methods.