Decay rates for stabilization of linear continuous-time systems with random switching. (English) Zbl 1425.93228
Summary: For a class of linear switched systems in continuous time a controllability condition implies that state feedbacks allow to achieve almost sure stabilization with arbitrary exponential decay rates. This is based on the multiplicative ergodic theorem applied to an associated system in discrete time. This result is related to the stabilizability problem for linear persistently excited systems.
MSC:
| 93D15 | Stabilization of systems by feedback |
| 93B05 | Controllability |
| 93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |
| 93C05 | Linear systems in control theory |
Keywords:
random switching; almost sure stabilization; arbitrary rate of convergence; Lyapunov exponents; persistent excitation; multiplicative ergodic theoremReferences:
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