3,459 research outputs found
Efficient Method for Computing Lower Bounds on the -radius of Switched Linear Systems
This paper proposes lower bounds on a quantity called -norm joint
spectral radius, or in short, -radius, of a finite set of matrices. Despite
its wide range of applications to, for example, stability analysis of switched
linear systems and the equilibrium analysis of switched linear economical
models, algorithms for computing the -radius are only available in a very
limited number of particular cases. The proposed lower bounds are given as the
spectral radius of an average of the given matrices weighted via Kronecker
products and do not place any requirements on the set of matrices. We show that
the proposed lower bounds theoretically extend and also can practically improve
the existing lower bounds. A Markovian extension of the proposed lower bounds
is also presented
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
Disease spread over randomly switched large-scale networks
In this paper we study disease spread over a randomly switched network, which
is modeled by a stochastic switched differential equation based on the so
called -intertwined model for disease spread over static networks. Assuming
that all the edges of the network are independently switched, we present
sufficient conditions for the convergence of infection probability to zero.
Though the stability theory for switched linear systems can naively derive a
necessary and sufficient condition for the convergence, the condition cannot be
used for large-scale networks because, for a network with agents, it
requires computing the maximum real eigenvalue of a matrix of size exponential
in . On the other hand, our conditions that are based also on the spectral
theory of random matrices can be checked by computing the maximum real
eigenvalue of a matrix of size exactly
Some simple but challenging Markov processes
In this note, we present few examples of Piecewise Deterministic Markov
Processes and their long time behavior. They share two important features: they
are related to concrete models (in biology, networks, chemistry,. . .) and they
are mathematically rich. Their math-ematical study relies on coupling method,
spectral decomposition, PDE technics, functional inequalities. We also relate
these simple examples to recent and open problems
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