Stability Analysis of Continuous-Time Switched Systems with a Random Switching Signal

This paper is concerned with the stability analysis of continuous-time switched systems with a random switching signal. The switching signal manifests its characteristics with that the dwell time in each subsystem consists of a fixed part and a random part. The stochastic stability of such switched systems is studied using a Lyapunov approach. A necessary and sufficient condition is established in terms of linear matrix inequalities. The effect of the random switching signal on system stability is illustrated by a numerical example and the results coincide with our intuition.Comment: 6 pages, 6 figures, accepted by IEEE-TA

Stabilizing Randomly Switched Systems

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 designComment: 22 pages. Submitte

Stability analysis for continuous-time switched systems with stochastic switching signals

This paper is concerned with the stability problem of randomly switched systems. By using the probability analysis method, the almost surely globally asymptotical stability and almost surely exponential stability are investigated for switched systems with semi-Markovian switching, Markovian switching and renewal process switching signals, respectively. Two examples are presented to demonstrate the effectiveness of the proposed results, in which an example of consensus of multi-agent systems with nonlinear dynamics is taken into account

Pinning dynamic systems of networks with Markovian switching couplings and controller-node set

In this paper, we study pinning control problem of coupled dynamical systems with stochastically switching couplings and stochastically selected controller-node set. Here, the coupling matrices and the controller-node sets change with time, induced by a continuous-time Markovian chain. By constructing Lyapunov functions, we establish tractable sufficient conditions for exponentially stability of the coupled system. Two scenarios are considered here. First, we prove that if each subsystem in the switching system, i.e. with the fixed coupling, can be stabilized by the fixed pinning controller-node set, and in addition, the Markovian switching is sufficiently slow, then the time-varying dynamical system is stabilized. Second, in particular, for the problem of spatial pinning control of network with mobile agents, we conclude that if the system with the average coupling and pinning gains can be stabilized and the switching is sufficiently fast, the time-varying system is stabilized. Two numerical examples are provided to demonstrate the validity of these theoretical results, including a switching dynamical system between several stable sub-systems, and a dynamical system with mobile nodes and spatial pinning control towards the nodes when these nodes are being in a pre-designed region.Comment: 9 pages; 3 figure

On Time-Varying Delayed Stochastic Differential Systems with Non-Markovian Switching Parameters

This paper focuses on time-varying delayed stochastic differential systems with stochastically switching parameters formulated by a unified switching behavior combining a discrete adapted process and a Cox process. Unlike prior studies limited to stationary and ergodic switching scenarios, our research emphasizes non-Markovian, non-stationary, and non-ergodic cases. It arrives at more general results regarding stability analysis with a more rigorous methodology. The theoretical results are validated through numerical examples

On Stochastic ISS of Time-Varying Switched Systems with Generic Lévy Switching Signals

Switched systems in which switching among subsystems occurs at random time instants find numerous applications in engineering. Stability analysis of such systems, however, is quite challenging. This paper investigates the stochastic input-to-state stability of this class of switched systems. The random switching instants are modeled by a non-decreasing, positive, and real-valued Levy process, which, at every time instant, selects the active subsystem from a family of deterministic systems. No assumption on the stability of subsystems is presumed; they can be stable or unstable. Stochastic properties of the switching signal are coupled with a family of Lyapunov-like functions to obtain a sufficient condition for stochastic input-to-state stability