Parameter-dependent Polynomial Control for Nonlinear Time-Varying Systems

Abstract

In this paper, a Parameter-Dependent Polynomial Fuzzy (PDPF) control issue of the nonlinear time-varying system is discussed via Sum-Of-Square (SOS) technology. Recently, a new type of fuzzy model named PDPF model is proposed by combining Takagi-Sugeno (T-S) fuzzy model, polynomial representation and Linear Parameter Varying (LPV) description. For the stabilization issue of nonlinear time-varying system, the PDPF controller is designed based on Parallel Distributed Compensation (PDC) method. However, stability issue of PDPF model is often more complex and difficult than one of the traditional Takagi-Sugeno fuzzy model since the nonconvex problem caused by the coupling of variables. To avoid the nonconvex term, a parameter-dependent positive definite matrix in Lyapunov function is adopted to derive the stability criterion. Besides, the convex combination is employed to eliminate the restriction of time-varying parameters. Thus, the sufficient conditions are derived into the SOS form and solved by the SOSTOOLS. Finally, the simulation results of the nonlinear time-varying system are provided to verify the PDPF controller design method.