Article

# Stability Analysis and Control Design for 2-D Fuzzy Systems via Basis-dependent Lyapunov Functions

(Impact Factor: 1.62). 10/2011; 24(3). DOI: 10.1007/s11045-011-0166-z

ABSTRACT

This paper investigates the problem of stability analysis and stabilization for two-dimensional (2-D) discrete fuzzy systems. The 2-D fuzzy system model is established based on the Fornasini-Marchesini local state-space (FMLSS) model, and a control design procedure is proposed based on a relaxed approach in which basis-dependent Lyapunov functions are used. First, nonquadratic stability conditions are derived by means of linear matrix inequal-ity (LMI) technique. Then, by introducing an additional instrumental matrix variable, the stabilization problem for 2-D fuzzy systems is addressed, with LMI conditions obtained for the existence of stabilizing controllers. Finally, the effectiveness and advantages of the proposed design methods based on basis-dependent Lyapunov functions are shown via two examples.

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Available from: Chen Xiaoming
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• "The issues of stability and stabilization of 2-D linear systems have been successfully investigated, and a rich body of literature is now available (see e.g. Benzaouia et al. 2011; Chen et al. 2011; Fan and Wen 2001, 2002; Pandolfi 1984; Hmamed et al. 2008; Xu et al. 2004; Lam et al. 2004 and the references therein). Since time delay frequently occurs in practical systems and is often a source of degradation or instability in system performance, the study on 2-D systems with state delays has also attracted many researchers, and some useful results on such systems have been reported in the literature "
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ABSTRACT: This paper investigates the ℓ 2 - ℓ ∞ filtering problem of T-S fuzzy systems with multiple time-varying delays. First, by the Lyapunov-Krasovskii functional approach and free-weighting matrix method, a delay-dependent sufficient condition on ℓ 2 - ℓ ∞ -disturbance attenuation is presented, in which both stability and prescribed ℓ 2 - ℓ ∞ performance are required to be achieved for the filtering-error systems. Then, based on the condition, the full-order and reduced-order delay-dependent ℓ 2 - ℓ ∞ filter design schemes for T-S fuzzy multiple time-varying delays systems are developed in terms of linear matrix inequality (LMI). Finally, an example is given to illustrate the effectiveness of the result.
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ABSTRACT: This paper is concerned with the problem of H ∞ control for uncertain two-dimensional (2-D) state delay systems described by the Roesser model. Based on a summation inequality, a sufficient condition to have a delay-dependent H ∞ noise attenuation for this 2-D system is given in terms of linear matrix inequalities (LMIs). A delay-dependent optimal state feedback H ∞ controller is obtained by solving an LMI optimization problem. Finally, a simulation example of thermal processes is given to illustrate the effectiveness of the proposed results.
No preview · Article · Jun 2012 · Circuits Systems and Signal Processing