2,783 research outputs found
Stabilizing Scheduling Policies for Networked Control Systems
This paper deals with the problem of allocating communication resources for
Networked Control Systems (NCSs). We consider an NCS consisting of a set of
discrete-time LTI plants whose stabilizing feedback loops are closed through a
shared communication channel. Due to a limited communication capacity of the
channel, not all plants can exchange information with their controllers at any
instant of time. We propose a method to find periodic scheduling policies under
which global asymptotic stability of each plant in the NCS is preserved. The
individual plants are represented as switched systems, and the NCS is expressed
as a weighted directed graph. We construct stabilizing scheduling policies by
employing cycles on the underlying weighted directed graph of the NCS that
satisfy appropriate contractivity conditions. We also discuss algorithmic
design of these cycles
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 feedback stabilization of linear switched systems via switching signal control
Motivated by recent applications in control theory, we study the feedback
stabilizability of switched systems, where one is allowed to chose the
switching signal as a function of in order to stabilize the system. We
propose new algorithms and analyze several mathematical features of the problem
which were unnoticed up to now, to our knowledge. We prove complexity results,
(in-)equivalence between various notions of stabilizability, existence of
Lyapunov functions, and provide a case study for a paradigmatic example
introduced by Stanford and Urbano.Comment: 19 pages, 3 figure
On convergence of infinite matrix products with alternating factors from two sets of matrices
We consider the problem of convergence to zero of matrix products
with factors from two sets of matrices,
and , due to a suitable choice of
matrices . It is assumed that for any sequence of matrices
there is a sequence of matrices such that the
corresponding matrix product converges to zero.
We show that in this case the convergence of the matrix products under
consideration is uniformly exponential, that is, , where the constants and
do not depend on the sequence and the corresponding sequence
.Comment: 7 pages, 13 bibliography references, expanded Introduction and
Section 4 "Remarks and Open Questions", accepted for publication in Discrete
Dynamics in Nature and Societ
A Gel'fand-type spectral radius formula and stability of linear constrained switching systems
Using ergodic theory, in this paper we present a Gel'fand-type spectral
radius formula which states that the joint spectral radius is equal to the
generalized spectral radius for a matrix multiplicative semigroup \bS^+
restricted to a subset that need not carry the algebraic structure of \bS^+.
This generalizes the Berger-Wang formula. Using it as a tool, we study the
absolute exponential stability of a linear switched system driven by a compact
subshift of the one-sided Markov shift associated to \bS.Comment: 16 pages; to appear in Linear Algebra and its Application
Feedback stabilization of dynamical systems with switched delays
We analyze a classification of two main families of controllers that are of
interest when the feedback loop is subject to switching propagation delays due
to routing via a wireless multi-hop communication network. We show that we can
cast this problem as a subclass of classical switching systems, which is a
non-trivial generalization of classical LTI systems with timevarying delays. We
consider both cases where delay-dependent and delay independent controllers are
used, and show that both can be modeled as switching systems with unconstrained
switchings. We provide NP-hardness results for the stability verification
problem, and propose a general methodology for approximate stability analysis
with arbitrary precision. We finally give evidence that non-trivial design
problems arise for which new algorithmic methods are needed
On stabilizability conditions for discrete-time switched linear systems
International audienceIn this paper we consider the stabilizability property for discrete-time switched linear systems. Novel conditions, in LMI form, are presented that permit to combine generality with computational affordability. The relations and implications between different conditions, new ones and taken from literature, for stabilizability are analyzed to infer and compare their conservatism and their complexity
An Unknown Input Multi-Observer Approach for Estimation and Control under Adversarial Attacks
We address the problem of state estimation, attack isolation, and control of
discrete-time linear time-invariant systems under (potentially unbounded)
actuator and sensor false data injection attacks. Using a bank of unknown input
observers, each observer leading to an exponentially stable estimation error
(in the attack-free case), we propose an observer-based estimator that provides
exponential estimates of the system state in spite of actuator and sensor
attacks. Exploiting sensor and actuator redundancy, the estimation scheme is
guaranteed to work if a sufficiently small subset of sensors and actuators are
under attack. Using the proposed estimator, we provide tools for reconstructing
and isolating actuator and sensor attacks; and a control scheme capable of
stabilizing the closed-loop dynamics by switching off isolated actuators.
Simulation results are presented to illustrate the performance of our tools.Comment: arXiv admin note: substantial text overlap with arXiv:1811.1015
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