2,521 research outputs found
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
On the gap between deterministic and probabilistic joint spectral radii for discrete-time linear systems
Given a discrete-time linear switched system associated
with a finite set of matrices, we consider the measures of its
asymptotic behavior given by, on the one hand, its deterministic joint spectral
radius and, on the other hand, its probabilistic
joint spectral radii for Markov random
switching signals with transition matrix and a corresponding invariant
probability . Note that is larger than or
equal to for every pair . In
this paper, we investigate the cases of equality of with either a single or with the
supremum of over and we aim at
characterizing the sets for which such equalities may occur
Mean square stabilization of discrete-time switching Markov jump linear systems
This paper consider a special class of hybrid system called switching Markov jump linear system. The system transition is governed by two rules. One is Markov chain and the other is a deterministic rule. Furthermore, the transition probability of the Markov chain is not only piecewise but also orchestrated by a deterministic switching rule. In this paper the mean square stability of the systems is studied when the deterministic switching is subject to two different dwell time conditions: having a lower bound and having both lower and high bounds. The main contributions of this paper are two relevant stability theorems for the systems under study. A numerical example is provided to demonstrate the theoretical results
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Almost sure stability of switching Markov Jump Linear Systems
Recently a special hybrid system called Switching
Markov Jump Linear System (SMJLS) is studied. A SMJLS is
subject to a deterministic switching and a stochastic Markovain switching. To extend the results already obtained and to investigate some new aspects of such systems, our main contributions in this paper are: (i) Transient analysis of Markov process, i.e. the expectations of the sojourn time, the activation number of any mode, and the number of switchings between any two modes; and (ii) Two sufficient conditions of the exponential almost sure stability for a general SMJLS. Different from previous work, which is a special case of our study, the transition rate matrix for the random Markov process in our study is not fixed, but varies when a deterministic switching takes place
Almost sure stability of discrete-time Markov Jump Linear Systems
This paper deals with transient analysis and almost sure stability for discrete-time Markov Jump Linear System (MJLS). The expectation of sojourn time and activation number of any mode, and switching number between any two modes of discrete-time MJLS are presented firstly. Then a result on transient behavior analysis of discrete-time MJLS is given. Finally a new deterministically testable condition for the exponential almost sure stability of discrete-time MJLS is proposed
Almost Sure Stabilization for Adaptive Controls of Regime-switching LQ Systems with A Hidden Markov Chain
This work is devoted to the almost sure stabilization of adaptive control
systems that involve an unknown Markov chain. The control system displays
continuous dynamics represented by differential equations and discrete events
given by a hidden Markov chain. Different from previous work on stabilization
of adaptive controlled systems with a hidden Markov chain, where average
criteria were considered, this work focuses on the almost sure stabilization or
sample path stabilization of the underlying processes. Under simple conditions,
it is shown that as long as the feedback controls have linear growth in the
continuous component, the resulting process is regular. Moreover, by
appropriate choice of the Lyapunov functions, it is shown that the adaptive
system is stabilizable almost surely. As a by-product, it is also established
that the controlled process is positive recurrent
On stability of randomly switched nonlinear systems
This article is concerned with stability analysis and stabilization of
randomly switched nonlinear 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 global asymptotic stability 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 Markov 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.Comment: 13 pages, no figures. A slightly modified version is scheduled to
appear in IEEE Transactions on Automatic Control, Dec 200
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