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CDC
2010
IEEE

Impulsive systems triggered by superposed renewal processes

10 years 6 months ago
Impulsive systems triggered by superposed renewal processes
We consider impulsive systems with several reset maps triggered by independent renewal processes, i.e., the intervals between jumps associated with a given reset map are identically distributed and independent of the other jump intervals. Considering linear dynamic and reset maps, we establish that mean exponential stability is equivalent to the spectral radius of an integral operator being less than one. The result builds upon a stochastic Lyapunov function approach which allows for providing stability conditions in the general case where the dynamic and the reset maps are non-linear. We also prove that the origin of an impulsive system with nonlinear dynamic and reset maps is stable with probability one if the linearization about zero equilibrium is mean exponentially stable, which justifies the importance of studying the linear case. The application of these results is illustrated in the context of networked control systems. The results in this paper permit the analysis of scenarios...
Duarte Antunes, João Pedro Hespanha, Carlos
Added 13 May 2011
Updated 13 May 2011
Type Journal
Year 2010
Where CDC
Authors Duarte Antunes, João Pedro Hespanha, Carlos Silvestre
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