Robust and non-fragile finite-time H∞ control for uncertain Markovian jump nonlinear systems.

This paper investigates the non-fragile and robust finite-time H∞ control problem for a class of uncertain Markovian jump nonlinear systems with bounded parametric uncertainties and norm-bounded disturbance. By employing stochastic analysis and linear matrix inequality techniques, sufficient criteria of stochastic finite-time boundedness and stochastic H∞ finite-time boundedness are first provided for the class of stochastic jump systems. Then, a controller is designed such that the class of stochastic nonlinear dynamics are stochastically finite-time bounded and have an H∞ attention performance level by utilizing matrix decomposition approach. Furthermore, the analysis and design of non-fragile and robust finite-time controller are provided to guarantee that the class of uncertain stochastic systems are stochastically finite-time boundeded with a prescribed attention index by using non-fragile control technique. In addition, we also deal with the analysis and design of stochastic finite-time stability and stochastic finite-time stabilization. All criterions can be characterized in terms of linear matrix inequalities. Finally, two examples are also given to illustrate the effectiveness of obtained results.