TS Fuzzy Model-Based Controller Design for a Class of Nonlinear Systems Including Nonsmooth Functions

Abstract

This paper proposes a novel robust controller design for a class of nonlinear systems including hard nonlinearity functions. The proposed approach is based on Takagi–Sugeno (TS) fuzzy modeling, nonquadratic Lyapunov function, and nonparallel distributed compensation scheme. In this paper, a novel TS modeling of the nonlinear dynamics with signum functions is proposed. This model can exactly represent the original nonlinear system with hard nonlinearity while the discontinuous signum functions are not approximated. Based on the bounded-input-bounded-output stability scheme and ${L_{1}}$ performance criterion, new robust controller design conditions in terms of linear matrix inequalities are derived. Three practical case studies, electric power steering system, a helicopter model and servo-mechanical system, are presented to demonstrate the importance of such class of nonlinear systems comprising signum function. Furthermore, to show the superiorities of the proposed approach, it is applied to these systems; and, the experimental real-time hardware-in-the-loop results are compared with the published literature with the same topic.