5,388 research outputs found
On almost sure stability of hybrid stochastic systems with mode-dependent interval delays
This note develops a criterion for almost sure stability of hybrid stochastic systems with mode-dependent interval time delays, which improves an existing result by exploiting the relation between the bounds of the time delays and the generator of the continuous-time Markov chain. The improved result shows that the presence of Markovian switching is quite involved in the stability analysis of delay systems. Numerical examples are given to verify the effectiveness
Adaptive Backstepping Controller Design for Stochastic Jump Systems
In this technical note, we improve the results in a paper by Shi et al., in which problems of stochastic stability and sliding mode control for a class of linear continuous-time systems with stochastic jumps were considered. However, the system considered is switching stochastically between different subsystems, the dynamics of the jump system can not stay on each sliding surface of subsystems forever, therefore, it is difficult to determine whether the closed-loop system is stochastically stable. In this technical note, the backstepping techniques are adopted to overcome the problem in a paper by Shi et al.. The resulting closed-loop system is bounded in probability. It has been shown that the adaptive control problem for the Markovian jump systems is solvable if a set of coupled linear matrix inequalities (LMIs) have solutions. A numerical example is given to show the potential of the proposed techniques
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
A new twist for the simulation of hybrid systems using the true jump method
The use of stochastic models, in effect piecewise deterministic Markov
processes (PDMP), has become increasingly popular especially for the modeling
of chemical reactions and cell biophysics. Yet, exact simulation methods, for
the simulation of these models in evolving environments, are limited by the
need to find the next jumping time at each recursion of the algorithm. Here, we
report on a new general method to find this jumping time for the True Jump
Method. It is based on an expression in terms of ordinary differential
equations for which efficient numerical methods are available. As such, our new
result makes it possible to study numerically stochastic models for which
analytical formulas are not available thereby providing a way to approximate
the state distribution for example. We conclude that the wide use of event
detection schemes for the simulation of PDMPs should be strongly reconsidered.
The only relevant remaining question being the efficiency of our method
compared to the Fictitious Jump Method, question which is strongly case
dependent
Almost surely asymptotic stability of neutral stochastic differential delay equations with Markovian switching
The main aim of this paper is to discuss the almost surely asymptotic stability of the neutral stochastic differential delay equations (NSDDEs) with Markovian switching. Linear NSDDEs with Markovian switching and nonlinear examples will be discussed to illustrate the theory
Effects of cell cycle noise on excitable gene circuits
We assess the impact of cell cycle noise on gene circuit dynamics. For
bistable genetic switches and excitable circuits, we find that transitions
between metastable states most likely occur just after cell division and that
this concentration effect intensifies in the presence of transcriptional delay.
We explain this concentration effect with a 3-states stochastic model. For
genetic oscillators, we quantify the temporal correlations between daughter
cells induced by cell division. Temporal correlations must be captured properly
in order to accurately quantify noise sources within gene networks.Comment: 15 pages, 8 figure
On stabilization of bilinear uncertain time-delay stochastic systems with Markovian jumping parameters
Copyright [2002] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, we investigate the stochastic stabilization problem for a class of bilinear continuous time-delay uncertain systems with Markovian jumping parameters. Specifically, the stochastic bilinear jump system under study involves unknown state time-delay, parameter uncertainties, and unknown nonlinear deterministic disturbances. The jumping parameters considered here form a continuous-time discrete-state homogeneous Markov process. The whole system may be regarded as a stochastic bilinear hybrid system that includes both time-evolving and event-driven mechanisms. Our attention is focused on the design of a robust state-feedback controller such that, for all admissible uncertainties as well as nonlinear disturbances, the closed-loop system is stochastically exponentially stable in the mean square, independent of the time delay. Sufficient conditions are established to guarantee the existence of desired robust controllers, which are given in terms of the solutions to a set of either linear matrix inequalities (LMIs), or coupled quadratic matrix inequalities. The developed theory is illustrated by numerical simulatio
Robust normalization and guaranteed cost control for a class of uncertain singular Markovian jump systems via hybrid impulsive control
This paper investigates the problem of robust normalization and guaranteed cost control for a class of uncertain singular Markovian jump systems. The uncertainties exhibit in both system matrices and transition rate matrix of the Markovian chain. A new impulsive and proportional-derivative control strategy is presented, where the derivative gain is to make the closed-loop system of the singular plant to be a normal one, and the impulsive control part is to make the value of the Lyapunov function does not increase at each time instant of the Markovian switching. A linearization approach via congruence transformations is proposed to solve the controller design problem. The cost function is minimized via solving an optimization problem under the designed control scheme. Finally, three examples (two numerical examples and an RC pulse divider circuit example) are provided to illustrate the effectiveness and applicability of the proposed methods
Stability of stochastic impulsive differential equations: integrating the cyber and the physical of stochastic systems
According to Newton's second law of motion, we humans describe a dynamical
system with a differential equation, which is naturally discretized into a
difference equation whenever a computer is used. The differential equation is
the physical model in human brains and the difference equation the cyber model
in computers for the dynamical system. The physical model refers to the
dynamical system itself (particularly, a human-designed system) in the physical
world and the cyber model symbolises it in the cyber counterpart. This paper
formulates a hybrid model with impulsive differential equations for the
dynamical system, which integrates its physical model in real world/human
brains and its cyber counterpart in computers. The presented results establish
a theoretic foundation for the scientific study of control and communication in
the animal/human and the machine (Norbert Wiener) in the era of rise of the
machines as well as a systems science for cyber-physical systems (CPS)
Stability of hybrid stochastic retarded systems
Abstract-In the past few years, hybrid stochastic retarded systems (also known as stochastic retarded systems with Markovian switching), including hybrid stochastic delay systems, have been intensively studied. Among the key results, Mao et al. proposed the Razumikhin-type theorem on exponential stability of stochastic functional differential equations with Markovian switching and its application to hybrid stochastic delay interval systems. However, the importance of general asymptotic stability has not been considered. This paper is to study Razumikhin-type theorems on general theorem moment asymptotic stability of hybrid stochastic retarded systems. The proposed theorems apply to complex systems including some cases when the existing results cannot be used
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