Abstract
For discrete fuzzy descriptor systems with time-delays, the problem of designing fuzzy observers is investigated in this paper. Based on an equivalent transformation, discrete fuzzy descriptor systems with time-delays are converted into standard discrete systems with time-delays. Then, via linear matrix inequality (LMI) approach, both delay-dependent and delay-independent conditions for the existence of fuzzy state observers are obtained. Finally, two numerical examples are provided to illustrate the proposed method.
Highlights
For many practical engineering systems, increased productivity has led to new operating conditions, which are more challenging
A sufficient condition about existence of considered observer, which does not rely on time-delay, is presented by the following theorem
The first one is to design a fuzzy observer according to Theorem 4 and the second one illustrates Theorem 5
Summary
For many practical engineering systems, increased productivity has led to new operating conditions, which are more challenging. Utilizing the approach of linear matrix inequality (LMI), [14] investigated D-stability and nonfragile control for T-S fuzzy discrete-time descriptor systems with multiple delays. About stability analysis and stabilization for a class of discrete-time T-S fuzzy systems with time-varying state delay, a novel delay-partitioning method was developed in [18] and a stability condition, which is much less conservative than most existing results, was derived by the new idea. For a class of discretetime T-S fuzzy time-delay systems, the problem of reliable filter design with strict dissipativity was considered in [20] and a sufficient condition of reliable dissipativity analysis was proposed. This paper focuses on designing observers for discrete-time fuzzy descriptor systems with time-delays via LMI approach, which is often used. This paper mainly discusses observer design for discrete-time-delayed descriptor systems with T-S fuzzy model.
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