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This note is intended to investigate noise-to-state stability for random nonlinear systems with state-dependent switching. Under some mild and easily verified conditions, the existence of global solution to random switched systems can be proved. Based on a reasonable requirement for the random disturbance, the criteria on noise-to-state stability of random switched systems are presented by the aid of single Lyapunov function technique. The reasonability of the obtained results is illustrated by using a mechanical model in random vibration environment. [ABSTRACT FROM AUTHOR]

In this note, the fault detection filtering problem is solved for nonlinear switched stochastic system in the T-S fuzzy framework. Our attention is concentrated on the construction of a robust fault detection technique to the nonlinear switched system with Brownian motion. Based on observer-based fault detection fuzzy filter as a residual generator, the proposed fault detection is formulated as a fuzzy filtering problem. By the utilization of the average dwell time technique and the piecewise Lyapunov function technique, the fuzzy-parameter-dependent fault detection filters are designed that guarantee the resulted error system to be mean-square exponential stable with a weighted \mathcal H\infty error performance. Then, the corresponding solvability condition for the fault detection fuzzy filter is also established by the linearization procedure technique. Finally, simulation has been presented to show the effectiveness of the proposed fault detection technique. [ABSTRACT FROM AUTHOR]