Stability of Switched Systems on Randomly Switching Durations With Random Interaction Matrices

In this paper, we investigate the almost sure stability of switched systems on randomly switching durations simultaneously with randomly switching interaction matrices. We not only allow the interaction matrix on each switching duration to take values randomly from either a countable, an uncountable, or even an unbounded state space, but also allow the corresponding probability density function to be time varying with the switching. We provide an example to show the difference between the almost sure stability and the moment stability. Then, we establish several practical stability criteria for switched systems, which may have linear or nonlinear subsystems. These stability criteria also enable us to find suitable conditions for realizing almost sure synchronization in complex networks, such as small-world networks, with both randomly switching durations and a few switching couplings that take values randomly in either an uncountable or an unbounded state space.