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

Multidimensional Systems and Signal Processing (Impact Factor: 0.86). 10/2011; DOI: 10.1007/s11045-011-0166-z

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**ABSTRACT:**This paper deals with the problem of stability and stabilization of 2D delayed continuous systems with saturation on the control. Improved delay depedent stability condition taken from recent literature is firstly extended to the case of 2D systems. Second, delay depedent stabilizability condition is deduced. The synthesis of stabilizing saturating state feedback controllers for such systems is then given. A set of allowed delays for both directions of the state is computed. All involved conditions are given under LMI's formalism. Examples are worked to show the effectiveness of the approach.Circuits Systems and Signal Processing 03/2013; · 0.98 Impact Factor -
##### Article: A Frequency-Partitioning Approach to Stability Analysis of Two-Dimensional Discrete Systems

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**ABSTRACT:**Although there exist necessary and sufficient conditions for two-dimensional (2-D) discrete systems, their application scope is almost limited to system analysis only and no work has demonstrated their possible extension to system synthesis. In this paper, we propose a novel frequency-partitioning approach to analyzing stability of 2-D discrete state-space systems. A piecewise constant matrix function is introduced to approximate the solution to the frequency-dependent Lyapunov inequality, whose solvability is known to be equivalent to stability of a 2-D state-space model. Then by the generalized Kalman–Yakubovich–Popov Lemma, new stability conditions are derived for the Roesser model and the Fornasini–Marchesini (FM) first and second models, respectively. Stability criteria in the paper simultaneously overcome the drawbacks of the simple 2-D Lyapunov inequality approach and the existing necessary and sufficient conditions: (1) They are expressed in terms of linear matrix inequalities (LMIs), which are generally less conservative than the existing simple 2-D Lyapunov inequality-based results, and could be improved by increasing the partitioning number; (2) Since each of the LMIs corresponds to a simple 2-D Lyapunov inequality, they are more suitable for further development for system synthesis than the existing necessary and sufficient conditions, which is demonstrated by an illustrative application to state-feedback control of an uncertain FM second model.Multidimensional Systems and Signal Processing 01/2013; (accepted). · 0.86 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**This paper investigates the dynamic output feedback H ∞ stabilization problem for a class of discrete-time 2D (two-dimensional) switched systems represented by a model of FM LSS (Fornasini–Marchesini local state space) model. First, sufficient conditions for the exponential stability and weighted H ∞ disturbance attenuation performance of the underlying system are derived via the average dwell time approach. Then, based on the obtained results, dynamic output feedback controller is proposed to guarantee that the resulting closed-loop system is exponentially stable and has a prescribed disturbance attenuation level γ. Finally, two examples are provided to verify the effectiveness of the proposed method.Circuits Systems and Signal Processing 04/2014; 33(4). · 0.98 Impact Factor

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