Journal ArticleDOI
p th moment exponential stabilisation of hybrid stochastic differential equations by feedback controls based on discrete-time state observations with a time delay
Quanxin Zhu,Qiuyan Zhang +1 more
Reads0
Chats0
TLDR
In this article, the authors considered the stability of hybrid stochastic differential equations by feedback control based on discrete-time state observations and established an upper bound on the duration τ between two consecutive state observations.Abstract:
The authors are concerned with the stability of hybrid stochastic differential equations by feedback controls based on discrete-time state observations. Under some reasonable conditions, they establish an upper bound on the duration τ between two consecutive state observations. Moreover, we can design the discrete-time state feedback control to stabilise the given hybrid stochastic differential equations in the sense of p
th moment exponential stability by developing a new theory. In comparison to the results given in the previous literature, this study has two new characteristics: (i) the stability criterion concerns p
th moment exponential stability, which is different from the existing works; (ii) discrete-time state observations depend on time delays.read more
Citations
More filters
Journal ArticleDOI
Stabilization of Stochastic Nonlinear Delay Systems With Exogenous Disturbances and the Event-Triggered Feedback Control
TL;DR: This note establishes the input-to-state practically exponential mean-square stability of the suggested system by designing the feedback gain matrix and the event-triggered feedback controller, which is expressed in terms of linear matrix inequalities.
Journal ArticleDOI
Reliable asynchronous sampled-data filtering of T–S fuzzy uncertain delayed neural networks with stochastic switched topologies
TL;DR: The intermittent fault-tolerance scheme is taken into fully account in designing a reliable asynchronous sampled-data controller, which ensures such that the resultant neural networks is asymptotically stable.
Journal ArticleDOI
Stability analysis of stochastic delayed complex networks with multi-weights based on Razumikhin technique and graph theory
Chunmei Zhang,Bang-Sheng Han +1 more
TL;DR: In this article, a novel kind of stochastic delayed complex networks with multi-weights (SDCNMW) is considered, and a global Lyapunov functional is constructed by a graph-theoretical approach based on Kirchhoff's matrix tree theorem.
Journal ArticleDOI
Self-Triggered State-Feedback Control for Stochastic Nonlinear Systems With Markovian Switching
Wenjuan Xie,Quanxin Zhu +1 more
TL;DR: A self-triggered sampling rule to overcome difficulty in state-feedback control scheme for nonlinear stochastic systems with Markovian switching and establishes a novel lemma to estimate the lower bound and upper bound of second-moment for state and error.
Journal ArticleDOI
Stability Criteria for Impulsive Stochastic Functional Differential Systems With Distributed-Delay Dependent Impulsive Effects
Wei Hu,Quanxin Zhu +1 more
TL;DR: This short note considers time-varying stochastic functional differential systems with distributed-delay dependent impulsive effects, and some stability criteria for such systems are established by developing some inequality techniques and using Lyapunov approach.
References
More filters
Book
Stochastic Differential Equations with Markovian Switching
Xuerong Mao,Chenggui Yuan +1 more
TL;DR: This textbook provides the first systematic presentation of the theory of stochastic differential equations with Markovian switching at an introductory level but emphasizes current advanced level research trends.
Journal ArticleDOI
Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control
Y. Ji,Howard J. Chizeck +1 more
TL;DR: In this paper, necessary and sufficient conditions for the existence of finite cost, constant, stabilizing controls for the infinite-time Markovian jump linear quadratic (JLQ) problem are established.
Book
Jump linear systems in automatic control
Abstract: This book is a monograph on hybrid parameter processes that are characterized by the presence of a discrete parameter and continuous variables. The author considers stochastic models in which the future control trajectories and the present solution do not determine completely the future of the system. The special stochastic processes and systems treated by the author are characterized by random transitions between different regimes, and this randomness primarily occurs through its discrete parameters. The book consists of eight chapters and two appendices. The appendices present brief summaries of basic probability, random processes, optima1 filtering, stochastic stability, stochastic maximum principles, matrix maximum principles, and stochastic dynamic programming. Readers might find it useful to consult references on applied probability and Markov processes before reading the eight chapters of this book. The first chapter introduces the reader to hybrid dynamic models by means of examples from target tracking, manufacturing processes, solar thermal receivers, and fault-tolerant control systems. Chapter 2 examines the global controllability and relative and stochastic stability of hybrid parameter systems. Also included in Chapter 2 are the concepts of Liapunov function and Liapunov exponents, observability, and detectability. Chapter 3 considers control optimization, jump linear quadratic regulators derived from maximum principles and dynamic programming, asymptotic behavior of quadratic regulators, suboptima1 solutions, optima1 switching output feedback, and algorithms for the optimization and evaluation of regulators for jump quadratic systems. The robustness, costs and their distribution, bound costs, and minimax solutions of jump linear systems are treated in Chapter 4, while the jump linear quadratic Gaussian problem is analyzed in some detail with Karman filtering and Poisson impulsive disturbances in Chapter 5. Optimal filtering, Wiener-driven oscillations, filter performance, and point-process observations are considered in Chapter 6. Chapter 7 deals with control under regime uncertainty, stability, control optimization, and regime estimation filters. The final chapter, Chapter 8, considers extensions of hybrid systems, non-Markovian processes, wide-band hybrid models, and extensions of the jump linear systems presented in the previous seven chapters. The book contains many theorems and proofs, is well illustrated with examples, and covers the material in depth. It is relatively free of typographical errors except that pages 206 and 207 have been interchanged.
Journal ArticleDOI
Stability of stochastic differential equations with Markovian switching
TL;DR: In this paper, the authors discuss the exponential stability of nonlinear stochastic differential equations with Markovian switching and show that the stability can be improved by using Markovians.
Journal ArticleDOI
Stability Analysis of Markovian Jump Stochastic BAM Neural Networks With Impulse Control and Mixed Time Delays
Quanxin Zhu,Jinde Cao +1 more
TL;DR: A linear matrix inequality approach is developed to derive some novel sufficient conditions that guarantee the exponential stability in the mean square of the equilibrium point of a class of impulsive stochastic bidirectional associative memory neural networks with both Markovian jump parameters and mixed time delays.