Robust H∞ output feedback control for polynomial discrete-time systems

This paper aims to design a robust output feedback controller with $H_{\infty }$ performance for polynomial discrete-time systems (PDTS). This is due to the lack of research available on PDTS’ output feedback control especially when uncertainty is considered in the system. To be specific, the norm-bounded uncertainties are considered instead of polytopic uncertainties and then a so-called ‘$scaled$’ system is established to relate the robust $H_{\infty }$ and the nonlinear $H_{\infty }$ output feedback control problem. The integrator approach is introduced to overcome the nonconvexity issue when the polynomial Lyapunov function is selected. The controller is obtained by solving the sufficient conditions which are formulated in Polynomial Matrix Inequalities (PMIs) which is then converted into Sum of Squares (SOS) form. Semidefinite Programming (SDP) is used to obtain the results. Finally, the efficacy of the method is shown through numerical examples.