This article addresses the $H_{\infty }$ stabilization problems for a class of nonlinear distributed parameter systems which is described by the first-order hyperbolic partial differential equations (PDEs). First, the first-order… Click to show full abstract
This article addresses the $H_{\infty }$ stabilization problems for a class of nonlinear distributed parameter systems which is described by the first-order hyperbolic partial differential equations (PDEs). First, the first-order hyperbolic PDE systems are identified as a polynomial fuzzy PDE system and the polynomial fuzzy controller for the polynomial fuzzy PDE system is proposed. By utilizing the proposed homogeneous polynomial Lyapunov functional, Euler’s homogeneous function theorem, and the proposed theorems, a spatial derivative sum-of-squares (SDSOS) exponential stabilization condition is proposed. In addition, a recursive algorithm for the SDSOS exponential stabilization condition is developed to find the feasible solution. Furthermore, in order to reduce the conservatism of the proposed results, a relaxed $H_{\infty }$ stabilization condition for the polynomial fuzzy PDE system is provided. Finally, the nonisothermal plug-flow reactor (PFR) is used to demonstrate the effectiveness and feasibility of the proposed method.
