742 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
Pinning dynamic systems of networks with Markovian switching couplings and controller-node set
In this paper, we study pinning control problem of coupled dynamical systems
with stochastically switching couplings and stochastically selected
controller-node set. Here, the coupling matrices and the controller-node sets
change with time, induced by a continuous-time Markovian chain. By constructing
Lyapunov functions, we establish tractable sufficient conditions for
exponentially stability of the coupled system. Two scenarios are considered
here. First, we prove that if each subsystem in the switching system, i.e. with
the fixed coupling, can be stabilized by the fixed pinning controller-node set,
and in addition, the Markovian switching is sufficiently slow, then the
time-varying dynamical system is stabilized. Second, in particular, for the
problem of spatial pinning control of network with mobile agents, we conclude
that if the system with the average coupling and pinning gains can be
stabilized and the switching is sufficiently fast, the time-varying system is
stabilized. Two numerical examples are provided to demonstrate the validity of
these theoretical results, including a switching dynamical system between
several stable sub-systems, and a dynamical system with mobile nodes and
spatial pinning control towards the nodes when these nodes are being in a
pre-designed region.Comment: 9 pages; 3 figure
On input-to-state stability of stochastic retarded systems with Markovian switching
This note develops a Razumikhin-type theorem on pth moment input-to-state stability of hybrid stochastic retarded systems (also known as stochastic retarded systems with Markovian switching), which is an improvement of an existing result. An application to hybrid stochastic delay systems verifies the effectiveness of the improved result
Delay-dependent robust stability of stochastic delay systems with Markovian switching
In recent years, stability of hybrid stochastic delay systems, one of the important issues in the study of stochastic systems, has received considerable attention. However, the existing results do not deal with the structure of the diffusion but estimate its upper bound, which induces conservatism. This paper studies delay-dependent robust stability of hybrid stochastic delay systems. A delay-dependent criterion for robust exponential stability of hybrid stochastic delay systems is presented in terms of linear matrix inequalities (LMIs), which exploits the structure of the diffusion. Numerical examples are given to verify the effectiveness and less conservativeness of the proposed method
Backstepping controller design for a class of stochastic nonlinear systems with Markovian switching
A more general class of stochastic nonlinear systems with irreducible homogenous Markovian switching are considered in this paper. As preliminaries, the stability criteria and the existence theorem of strong solutions are first presented by using the inequality of mathematic expectation of a Lyapunov function. The state-feedback controller is designed by regarding Markovian switching as constant such that the closed-loop system has a unique solution, and the equilibrium is asymptotically stable in probability in the large. The output-feedback controller is designed based on a quadratic-plus-quartic-form Lyapunov function such that the closed-loop system has a unique solution with the equilibrium being asymptotically stable in probability in the large in the unbiased case and has a unique bounded-in-probability solution in the biased case
Quantum control theory and applications: A survey
This paper presents a survey on quantum control theory and applications from
a control systems perspective. Some of the basic concepts and main developments
(including open-loop control and closed-loop control) in quantum control theory
are reviewed. In the area of open-loop quantum control, the paper surveys the
notion of controllability for quantum systems and presents several control
design strategies including optimal control, Lyapunov-based methodologies,
variable structure control and quantum incoherent control. In the area of
closed-loop quantum control, the paper reviews closed-loop learning control and
several important issues related to quantum feedback control including quantum
filtering, feedback stabilization, LQG control and robust quantum control.Comment: 38 pages, invited survey paper from a control systems perspective,
some references are added, published versio
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
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Nonlinear filtering for state delayed systems with Markovian switching
Copyright [2003] 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.This paper deals with the filtering problem for a general class of nonlinear time-delay systems with Markovian jumping parameters. The nonlinear time-delay stochastic systems may switch from one to the others according to the behavior of a Markov chain. The purpose of the problem addressed is to design a nonlinear full-order filter such that the dynamics of the estimation error is guaranteed to be stochastically exponentially stable in the mean square. Both filter analysis and synthesis problems are investigated. Sufficient conditions are established for the existence of the desired exponential filters, which are expressed in terms of the solutions to a set of linear matrix inequalities (LMIs). The explicit expression of the desired filters is also provided. A simulation example is given to illustrate the design procedures and performances of the proposed method
Algebraic Invariance Conditions in the Study of Approximate (Null-)Controllability of Markov Switch Processes
We aim at studying approximate null-controllability properties of a
particular class of piecewise linear Markov processes (Markovian switch
systems). The criteria are given in terms of algebraic invariance and are
easily computable. We propose several necessary conditions and a sufficient
one. The hierarchy between these conditions is studied via suitable
counterexamples. Equivalence criteria are given in abstract form for general
dynamics and algebraic form for systems with constant coefficients or
continuous switching. The problem is motivated by the study of lysis phenomena
in biological organisms and price prediction on spike-driven commodities.Comment: Mathematics of Control, Signals, and Systems, Springer Verlag
(Germany), 2015, online first
http://link.springer.com/article/10.1007/s00498-015-0146-
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