Almost sure stability and stabilization of discrete-time stochastic systems

Huang, Lirong; Hjalmarsson, Håkan; Koeppl, Heinz

doi:10.1016/j.sysconle.2015.05.005

Cited by 17 publications

(15 citation statements)

References 39 publications

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“…Stochastic difference equation (75), also called discrete-time stochastic systems [29], has been intensively studied over the past a few decades. In practical applications, it is natural to form and use some continuous-time extensions of the discrete approximation {X k } such as X(t) defined by [20,43]…”

Section: Exponential Stability Of Cpsmentioning

confidence: 99%

“…On the other hand, whenever a computer is used in measurement, computation, signal processing or control applications, the data, signals and systems involved are naturally described as discrete-time processes. Prevalent employments of computers and wide use of stochastic modelling have greatly boosted not only popularity of numerical methods for SDEs (see [19,20,34,41,48,50]), but also investigations on stochastic systems described by stochastic difference equations, including those many discretizations of SDEs, over the recent years (see, e.g., [9,28,29,53]), because of their various applications. From the behaviour of the discrete-time stochastic processes generated by some numerical scheme that are the approximate realizations of the exact solution, one would learn and/or infer some dynamical properties of the underlying SDE (see, e.g., [2,52]).…”

Section: Introductionmentioning

confidence: 99%

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Stability of cyber-physical systems of numerical methods for stochastic differential equations: integrating the cyber and the physical of stochastic systems

Huang

2019

Preprint

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This paper proposes a novel framework for theory of cyberphysical systems (CPS) as well as numerical study of stochastic differential equations (SDEs), which formulates a hybrid system with stochastic impulsive differential equations (SiDEs) to descibe the integrated dynamics of the physical and the cyber parts of the system that are represented by the exact and numerical solutions of an SDE, respectively, unlike in the literature where they are linked by inequalities. This systematic representation provides not only a holistic view but also a seamless, fully synergistic integration of the cyber subsystem/the numerical method with the physical subsystem/the SDE. To establish a foundation of the proposed framework, this paper initiates the study of a new and general class of SiDEs and develop by Lyapunov methods a stability theory for the general class of SiDEs. Applying the established theory, this paper studies the test problem (Q1) how to reproduce the pth moment exponential stability of the underlying physical system/SDE in the cyber counterpart/the widely-used Eular-Maruyama method and the converse (Q2) whether the pth moment exponential stability of the underlying physical system/SDE can be inferred from that of the cyber counterpart/the numerical method. The proposed theory removes the principal barrier to developing CPS and establishes a new systems science that comprehends cyber and physical resources in a single unified framework. As an application, this paper presents the cyber-physical/numerical Lyapunov-Itô inequality for linear systems, which is the necessary and sufficient condition for mean-square exponential stability of the physical system/the SDE, its cyber counterpart/the Eular-Maruyama method, and the resulting CPS/SiDE. This work initiates the studies of systems numerics and the systems science for CPS, in which there are many open and challenging problems.

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Section: Exponential Stability Of Cpsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stability of cyber-physical systems of numerical methods for stochastic differential equations: integrating the cyber and the physical of stochastic systems

Huang

2019

Preprint

Self Cite

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“…Recently, Reference 16 dealt with the

\sigma

‐error MS‐stability of semi‐Markov jump linear systems. Other nice results can be found, for example, almost sure stability and stabilization of nonlinear discrete‐time stochastic systems in Reference 17, MS‐exponential stability and stabilization for stochastic control systems with discrete‐time state feedbacks (SFs) in Reference 18, moment stability of nonlinear discrete stochastic systems with time‐delays in Reference 19 and the references therein. Recently, Reference 20 studied the optimal output feedback control and stabilization problems for discrete‐time multiplicative noise system with intermittent observations.…”

Section: Introductionmentioning

confidence: 96%

Mean‐square strong stability and stabilization of discrete‐time stochastic systems with multiplicative noises

Yan

2022

Intl J Robust & Nonlinear

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This article investigates the mean-square strong stability and stabilization of a discrete-time stochastic system corrupted by multiplicative noises. First, the definition of the mean-square (MS) strong stability is addressed to avoid overshoots in system dynamics, and two necessary and sufficient conditions for the MS-strong stability are derived. Moreover, the relationship between MS-strong stability and MS-stability is given. Second, some necessary and sufficient conditions of the MS-strong stabilization via state feedback (SF) and output feedback are obtained, respectively. Furthermore, analytical expressions of SF controller and static output feedback (SOF) controller are proposed, respectively. Finally, an equivalent design method for SOF controller and dynamic output feedback controller is presented.

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“…In [3], the infinite horizon mixed

H_{2} / H_{\infty}

control was solved for time‐varying stochastic discrete‐time systems under uniform detectability. A linear matrix inequality approach was developed for almost sure stabilisation of linear discrete‐time stochastic systems in [4].…”

Section: Introductionmentioning

confidence: 99%

Implicit iterative algorithms with a tuning parameter for discrete stochastic Lyapunov matrix equations

Zhang

Shao

2017

IET Control Theory & Applications

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Almost sure stability and stabilization of discrete-time stochastic systems

Cited by 17 publications

References 39 publications

Stability of cyber-physical systems of numerical methods for stochastic differential equations: integrating the cyber and the physical of stochastic systems

Stability of cyber-physical systems of numerical methods for stochastic differential equations: integrating the cyber and the physical of stochastic systems

Mean‐square strong stability and stabilization of discrete‐time stochastic systems with multiplicative noises

Implicit iterative algorithms with a tuning parameter for discrete stochastic Lyapunov matrix equations

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