Composite Fuzzy Control of Nonlinear Singularly Perturbed Systems

Abstract

This paper presents the composite fuzzy control to stabilize the nonlinear singularly perturbed (NSP) systems with guaranteed control performance. We use the Takagi-Sugeno (T-S) fuzzy model to construct the singularly perturbed fuzzy (SPF) systems. The corresponding fuzzy slow and fast subsystems of the original SPF system are also obtained. At first, a set of common positive-define matrices and the controller gains are determined by the Lyapunov stability theorem and linear matrix inequality (LMI) approach. Then, a sufficient condition is derived for the robust stabilization of NSP systems. The composite fuzzy control will stabilize the original NSP systems for all (0 ) and the allowable perturbation bound can be determined via some algebra inequalities. A practice example is adopted to demonstrate the feasibility and effectiveness of the proposed control scheme. Index Terms-control performance, linear matrix inequality (LMI), nonlinear singularly perturbed (NSP) systems, singularly perturbed fuzzy (SPF) systems, Takagi-Sugeno (T-S) fuzzy model.

Multiobjective Control for T–S Fuzzy Singularly Perturbed Systems

“…The design approaches given by [30] and [31] involve the separation of states into slow and fast ones, which limits the applications of these methods to standard SPSs. An H ∞ controller with the consideration of maximizing the bound for the singular perturbation parameter ε was designed in [32] by an LMI-based algorithm.…”

“…Among these papers, only H ∞ control was addressed in [26], [27], [30], and [31]. H ∞ control with pole placement constraints was investigated in [28] and [29].…”

“…Such a problem has been recognized by several researchers. Based on the separation of states into slow and fast ones, a composite fuzzy H ∞ controller was constructed in [30] and [31], and the upper bound for the singular perturbation parameter ε is then determined. In these results, the controller design procedures are not concerned with the bound of the singular perturbation parameter ε.…”

Robust ℋ∞Sampled-Data Control for Takagi-Sugeno Fuzzy Model with Singular Perturbation

“…특이섭동 현상은 도립진자 시스템의 관성모멘트 (inertia) [2], 터널다이오드 회로의 기생(parasitic) 인덕턴스 등 비선형시스템에서도 관찰된다 [3]. 선형시스템에서의 특이섭동은 다수 연구되었으며 [4][5][6][7], 비선형시스템, 특히 특이섭동 타카기-수게노(T-S) 퍼지모델의 제어에 관련된 연구도 수행되고 있다 [8][9][10].…”

H∞ Control for T‐S Fuzzy Singularly Perturbed Switched Systems

“…The resulting conditions in [11,[28][29][30][31] are only applicable to stabilizing the system and being with an ∞ performance for sufficiently small . Hence, some researchers have concentrated on the -bound design problem for fuzzy SPSs [32][33][34].…”