538 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
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
Static output-feedback stabilization of discrete-time Markovian jump linear systems: a system augmentation approach
This paper studies the static output-feedback (SOF) stabilization problem for discrete-time Markovian jump systems from a novel perspective. The closed-loop system is represented in a system augmentation form, in which input and gain-output matrices are separated. By virtue of the system augmentation, a novel necessary and sufficient condition for the existence of desired controllers is established in terms of a set of nonlinear matrix inequalities, which possess a monotonic structure for a linearized computation, and a convergent iteration algorithm is given to solve such inequalities. In addition, a special property of the feasible solutions enables one to further improve the solvability via a simple D-K type optimization on the initial values. An extension to mode-independent SOF stabilization is provided as well. Compared with some existing approaches to SOF synthesis, the proposed one has several advantages that make it specific for Markovian jump systems. The effectiveness and merit of the theoretical results are shown through some numerical example
Stability Optimization of Positive Semi-Markov Jump Linear Systems via Convex Optimization
In this paper, we study the problem of optimizing the stability of positive
semi-Markov jump linear systems. We specifically consider the problem of tuning
the coefficients of the system matrices for maximizing the exponential decay
rate of the system under a budget-constraint. By using a result from the matrix
theory on the log-log convexity of the spectral radius of nonnegative matrices,
we show that the stability optimization problem reduces to a convex
optimization problem under certain regularity conditions on the system matrices
and the cost function. We illustrate the validity and effectiveness of the
proposed results by using an example from the population biology
On exponential almost sure stability of random jump systems
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