An iterative Sum-of-Squares optimization for static output feedback of polynomial systems

Abstract

Abstract-This work proposes an iterative procedure for static output feedback of polynomial systems based on Sum-ofSquares optimization. Necessary and sufficient conditions for static output feedback stabilization of polynomial systems are formulated, both for the global and for the local stabilization case. Since the proposed conditions are bilinear with respect to the decision variables, an iterative procedure is proposed for the solution of the stabilization problem. Every iteration is shown to improve the performance with respect to the previous one, even if convergence to a local minimum might occur. Since polynomial Lyapunov functions and control laws are considered, a Sum-of-Squares optimization approach is adopted. A numerical example illustrates the results.

An Application of QSR-Dissipativity to the Problem of Static Output Feedback Robust Stabilization of Nonlinear Systems

“…The whole controller design procedure can be implemented in MATLAB R with well-known SDP tools (Löfberg (2004), Sturm (1999)). We consider the following version of a nonlinear system which was also analyzed in Baldi (2016) x…”