Mathematics – Optimization and Control
Scientific paper
2008-06-09
SIAM Journal on Control & Optimization, Vol 49, No. 5, pp. 2008-2031
Mathematics
Optimization and Control
22 pages. Submitted
Scientific paper
10.1137/080726720
This article is concerned with stability analysis and stabilization of randomly switched systems under a class of switching signals. The switching signal is modeled as a jump stochastic (not necessarily Markovian) process independent of the system state; it selects, at each instant of time, the active subsystem from a family of systems. Sufficient conditions for stochastic stability (almost sure, in the mean, and in probability) of the switched system are established when the subsystems do not possess control inputs, and not every subsystem is required to be stable. These conditions are employed to design stabilizing feedback controllers when the subsystems are affine in control. The analysis is carried out with the aid of multiple Lyapunov-like functions, and the analysis results together with universal formulae for feedback stabilization of nonlinear systems constitute our primary tools for control design
Chatterjee Debasish
Liberzon Daniel
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