1,825 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
Approximate Kalman-Bucy filter for continuous-time semi-Markov jump linear systems
The aim of this paper is to propose a new numerical approximation of the
Kalman-Bucy filter for semi-Markov jump linear systems. This approximation is
based on the selection of typical trajectories of the driving semi-Markov chain
of the process by using an optimal quantization technique. The main advantage
of this approach is that it makes pre-computations possible. We derive a
Lipschitz property for the solution of the Riccati equation and a general
result on the convergence of perturbed solutions of semi-Markov switching
Riccati equations when the perturbation comes from the driving semi-Markov
chain. Based on these results, we prove the convergence of our approximation
scheme in a general infinite countable state space framework and derive an
error bound in terms of the quantization error and time discretization step. We
employ the proposed filter in a magnetic levitation example with markovian
failures and compare its performance with both the Kalman-Bucy filter and the
Markovian linear minimum mean squares estimator
Recent advances on recursive filtering and sliding mode design for networked nonlinear stochastic systems: A survey
Copyright © 2013 Jun Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Some recent advances on the recursive filtering and sliding mode design problems for nonlinear stochastic systems with network-induced phenomena are surveyed. The network-induced phenomena under consideration mainly include missing measurements, fading measurements, signal quantization, probabilistic sensor delays, sensor saturations, randomly occurring nonlinearities, and randomly occurring uncertainties. With respect to these network-induced phenomena, the developments on filtering and sliding mode design problems are systematically reviewed. In particular, concerning the network-induced phenomena, some recent results on the recursive filtering for time-varying nonlinear stochastic systems and sliding mode design for time-invariant nonlinear stochastic systems are given, respectively. Finally, conclusions are proposed and some potential future research works are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grant nos. 61134009, 61329301, 61333012, 61374127 and 11301118, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant no. GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany
Compound Markov counting processes and their applications to modeling infinitesimally over-dispersed systems
We propose an infinitesimal dispersion index for Markov counting processes.
We show that, under standard moment existence conditions, a process is
infinitesimally (over-) equi-dispersed if, and only if, it is simple
(compound), i.e. it increases in jumps of one (or more) unit(s), even though
infinitesimally equi-dispersed processes might be under-, equi- or
over-dispersed using previously studied indices. Compound processes arise, for
example, when introducing continuous-time white noise to the rates of simple
processes resulting in Levy-driven SDEs. We construct multivariate
infinitesimally over-dispersed compartment models and queuing networks,
suitable for applications where moment constraints inherent to simple processes
do not hold.Comment: 26 page
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