Authors:
Ling Hou,
Anthony N. Michel,
Volume: 1, Page 2335 Paper number 1143
Abstract:
In the present paper we first formulate a general model for stochastic
dynamical systems that is suitable in the stability analysis of invariant
sets. This model is sufficiently general to include as special cases
most of the stochastic systems considered in the literature. We then
adapt several existing stability concepts to this model and we introduce
the notion of stability preserving mapping of stochastic dynamical
systems. Next, we establish a result which ensure that a function is
a stability preserving mapping, and we use this result in proving a
Comparison Stability Theorem for general stochastic dynamical systems.
We apply the Comparison Stability Theorem in the stability analysis
of dynamical systems determined by Ito differential equations.
Authors:
Patrick A. Florchinger,
Volume: 1, Page 2341 Paper number 9017
Abstract:
The purpose of this paper is to extend to stochastic differential systems
without unforced dynamics the stabilization techniques for controllable
driftless systems developed by Pomet.
Authors:
Ling Hou,
Anthony N. Michel,
Volume: 1, Page 2343 Paper number 1059
Abstract:
We study the stability properties of pulse-width-modulated (PWM) feedback
systems with stable plants, subjected to multiplicative and additive
random disturbances (modeled by the derivative of a Wiener process).
We show that when the parameters of the pulse-width modulator are within
a computable range and the random disturbances are sufficiently small,
then the PWM feedback system is globally asymptotically stable in the
pth mean. We also show that in the presence of additive disturbances,
such PWM feedback systems are bounded in the pth mean for arbitrarily
large disturbances.
Authors:
Marcelo D. Fragoso,
Jack Baczynski,
Volume: 1, Page 2349 Paper number 1673
Abstract:
This paper deals with Lyapunov equations for continuous-time Markov
jump linear systems (MJLS). Out of the bent which wends most of the
literature on MJLS, we focus here on the case in which the Markov chain
has a countably infinite state space. It is shown that the infinite
MJLS is stochastically stabilizable (SS) if and only if the associated
countably infinite coupled Lyapunov equations have a unique norm bounded
strictly positive definite solution. It is worth mentioning here that
this result do not hold for mean square stabilizability (MSS), since
SS and MSS are no longer equivalent in our set up. To some extent,tools
from operator theory in Banach space and, in particular, from semigroup
theory are the very technical underpinning of the paper.
Authors:
Eduardo F. Costa,
João B.R. do Val,
Volume: 1, Page 2355 Paper number 1942
Abstract:
This paper presents a new detectability concept for discrete-time Markov
jump linear systems with finite Markov state, which generalizes the
MS-detectability concept found in the literature. The new sense of
detectability can similarly assure that the solution of the coupled
algebraic Riccati equation associated to the quadratic control problem
is a stabilizing solution. In addition, the paper introduces a related
observability concept which also generalizes previous concepts. Tests
for detectability or observability are derived from the corresponding
definitions, that can be performed in a finite number of steps. An
illustrative example is included to show that a system may be detectable
in the new sense but not in the MS sense.
Authors:
Marcelo D. Fragoso,
Oswaldo L.V. Costa,
Volume: 1, Page 2361 Paper number 2013
Abstract:
Necessary and sufficient conditions for mean square stability(MSS)
of continuous-time linear systems subject to Markovian jumps in the
parameters and additive disturbances are established. We consider two
scenarios regarding the additive disturbances: the one in which the
system is driven by a Wiener process, and the one characterized by
functions in L2, which is the usual scenario for the H-Infinity approach.
For both cases it is shown that MSS is equivalent to asymptotic wide
sense stationarity (AWSS), to the spectrum of an augmented matrix
lying in the open left half plane, and to the existence of a solution
for a certain Lyapunov equation. Furthermore, it is proved that the
Lyapunov equation can be written down in two equivalent forms with
each one providing an easier-to-check sufficient condition. It is also
shown that MSS is equivalent to the state x(t) belonging to L2 whenever
the disturbances are in L-2. These results provide, inter alia, a
flexible theory, in a unified basis, for MSS of continuous-time Markovian
jump linear systems.
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