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Abstract
SUMMARY This paper is concerned with exploring an extended ap-proach for the stability analysis and synthesis for Markovian jump nonlin-ear systems (MJNLSs) via fuzzy control. The Takagi-Sugeno (T–S) fuzzymodel is employed to represent the MJNLSs with incomplete transitiondescription. In this paper, not all the elements of the rate transition matri-ces (RTMs), or probability transition matrices (PTMs) are assumed to beknown. By fully considering the properties of the RTMs and PTMs, suf-ficient criteria of stability and stabilization is obtained in both continuousand discrete-time. Stabilization conditions with a mode-dependent fuzzycontroller are derived for Markovian jump fuzzy systems in terms of linearmatrix inequalities (LMIs), which can be readily solved by using existingLMI optimization techniques. Finally, illustrative numerical examples areprovided to demonstrate the effectiveness of the proposed approach. key words: linear matrix inequality (LMI), Markovian jump fuzzy systems(MJFSs), stochastic stability, stabilization, rate transition matrix, proba-bility transition matrix
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