Stability Analysis and Fuzzy Control for Markovian Jump Nonlinear Systems with Partially Unknown Transition Probabilities

This Paper is concerned with exploring an extended approach for the stability analysis and synthesis for Markovian jump nonlinear systems (MJNLSs) via fuzzy control. The Takagi-Sugeno (T-S) fuzzy model is employed to represent the MJNLSs with incomplete transition description. In this paper, not all the elements of the rate transition matrices (RTMs), or probability transition matrices (PTMs) are assumed to be known. By fully considering the properties of the RTMs and PTMs, sufficient criteria of stability and stabilization is obtained in both continuous and discrete-time. Stabilization conditions with a mode-dependent fuzzy controller are derived for Markovian jump fuzzy systems in terms of linear matrix inequalities (LMIs), which can be readily solved by using existing LMI optimization techniques. Finally, illustrative numerical examples are provided to demonstrate the effectiveness of the proposed approach.