Stability of Stochastic Nonlinear Systems With State-Dependent Switching

Noise-to-state stability for random affine systems with state-dependent switching?

“…By a recursive procedure as similar to [15], we can construct a strong solution to the random switched system (10) in the maximal existence interval.…”

“…Stochastic switched systems have recently been the focus of attention in control engineering such as [13], [14]. The stability of stochastic nonlinear systems with state-dependent switching was investigated in [15], where the switching laws can be viewed as a closed-loop control. Exponential stability and almost sure exponential stability of stochastic systems with state-dependent switching was studied in [16].…”

“…By adopting the similar method as in [15], a strong solution to the random switched system is constructed based on the corresponding state-dependent switching signal. Because of switching behavior between individual subsystems, the smoothness (about time) of Lyapunov function is destroyed, which means that the stability results to random systems without switching are not suitable for random switched systems.…”

Stability analysis and stabilization of 2-D switched systems under arbitrary and restricted switchings

“…This type of systems can be used to describe many practical applications, such as mechanical systems, chemical processes, electronic circuits, transportation systems, computer controlled systems and communication systems. So far, stability analysis and switching stabilizability are the major concerns in the area of switched systems (Lin & Antsaklis, 2009;Wu, Cui, Shi, & Karimi, 2013). To date, two stability issues have been addressed in the literature, i.e., the stability under arbitrary switching (Vu & Morgansen, 2010) and the stability under restricted switching (Zhang & Gao, 2010).…”

Exponential Stability of Switched Time-varying Delayed Neural Networks with All Modes Being Unstable

“…However, the designing of the appropriate switching laws to keep the whole switched system stable is still an interesting and challenge problem [24][25][26][27][28][29]. In [25], the exponential stability of stochastic systems are investigated using the mode-dependent switching law.…”