Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/25246
Title: Stability analysis of discrete-time fuzzy-model-based control systems with time delay : time delay-independent approach
Authors: Lam, HK
Leung, FHF 
Keywords: Fuzzy control
Stability
Time delay
Issue Date: 2008
Publisher: Elsevier Science Bv
Source: Fuzzy sets and systems, 2008, v. 159, no. 8, p. 990-1000 How to cite?
Journal: Fuzzy Sets and Systems 
Abstract: This paper presents the stability analysis of discrete-time fuzzy-model-based control systems with time delays. To facilitate the stability analysis, the T-S fuzzy model is employed to represent the discrete-time nonlinear system. Due to the multiplication property of the fuzzy-model-based control system, the number of LMI-based stability conditions is p (p + 1) / 2 where p is the number of rules for the fuzzy model and fuzzy controller. Consequently, the computational demand for solving the solution to the stability conditions is very expensive, especially when the value of p is large. The problem becomes much worse when the relaxed stability conditions are formulated as huge matrices. The huge matrices incorporate the information of all the closed-loop subsystems, which may cause the solution of the LMI-based stability conditions difficult or even impossible to obtain owing to the limited computer power. In this paper, to reduce the computational demand, the fuzzy-model-based control system is divided into parts which the control input will handle separately. As a result, the multiplication property of the fuzzy-model-based control system can be removed, which effectively reduces the number of stability conditions to p and the computational demand for finding the solution can be reduced. LMI-based delay-independent stability conditions are derived using the Lyapunov-based approach. Simulation examples are given to illustrate the effectiveness of the proposed approach.
URI: http://hdl.handle.net/10397/25246
DOI: 10.1016/j.fss.2007.11.012
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