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On stability of randomly switched nonlinear systems (2005)
| Content Provider | CiteSeerX |
|---|---|
| Author | Chatterjee, Debasish Liberzon, Daniel |
| Abstract | Abstract—This note is concerned with stability analysis and stabilization of randomly switched systems. These systems may be regarded as piecewise deterministic stochastic systems: the discrete switches are triggered by a stochastic process which is independent of the state of the system, and between two consecutive switching instants the dynamics are deterministic. Our results provide sufficient conditions for almost sure stability and stability in the mean using Lyapunov-based methods when individual subsystems are stable and a certain “slow switching ” condition holds. This slow switching condition takes the form of an asymptotic upper bound on the probability mass function of the number of switches that occur between the initial and current time instants. This condition is shown to hold for switching signals coming from the states of finite-dimensional continuous-time Markov chains; our results, therefore, hold for Markovian jump systems in particular. For systems with control inputs, we provide explicit control schemes for feedback stabilization using the universal formula for stabilization of nonlinear systems. Index Terms—Almost sure and mean stochastic stability, random switching, stabilization, switched systems. I. |
| File Format | |
| Journal | IEEE Transactions on |
| Language | English |
| Publisher Date | 2005-01-01 |
| Access Restriction | Open |
| Subject Keyword | Nonlinear System Random Switching Explicit Control Scheme Finite-dimensional Continuous-time Markov Chain Feedback Stabilization Discrete Switch Universal Formula Sure Stability Control Input Sufficient Condition Probability Mass Function Individual Subsystem Current Time Instant Index Term Almost Sure Markovian Jump System Slow Switching Condition Mean Stochastic Stability Stochastic Process Stability Analysis Lyapunov-based Method Asymptotic Upper Bound Piecewise Deterministic Stochastic System |
| Content Type | Text |
| Resource Type | Article |
