Robust fuzzy control for nonlinear discrete-time systems with internal and external noises subject to multi-variance constraints and pole location constraints

Abstract

A novel robust fuzzy controller design problem subject to multi-variance constraints and pole location constraints for nonlinear discrete-time systems with internal and external noises is studied in this paper. Based on the Takagi-Sugeno fuzzy model, the nonlinear discrete-time systems are represented by blending many linear subsystems. The control performances considered in this paper include stability requirement, pole location constraint, individual state variance constraint, and minimum output variance. Applying the Lyapunov theory, a discrete-time robust fuzzy controller is designed based on parallel distributed compensation technology and the relevant conditions are deduced in the form of linear matrix inequalities. By solving these conditions, a discrete-time robust fuzzy controller can be obtained to satisfy the above performance constraints. At last, some simulations for controlling a nonlinear inverted pendulum system and a nonlinear ship steering system are provided to show the feasibility and applicability of the proposed robust fuzzy control method.