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Lyapunov Theorems for Semistability of Discrete-Time Stochastic Systems with Application to Network Consensus with Random Communication Noise

机译：Lyapunov定理，用于不同时间随机系统的应用与随机通信噪声的网络共识

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This paper develops Lyapunov and converse Lyapunov theorems for discrete-time stochastic semistable nonlinear dynamical systems expressed by Itô-type difference equations possessing a continuum of equilibria. Specifically, we provide necessary and sufficient Lyapunov conditions for stochastic semistability and show that stochastic semistability implies the existence of a continuous Lyapunov function whose difference operator involves a discrete-time analog of the infinitesimal generator for continuous-time Ito dynamical systems and decreases along the dynamical system sample solution sequences satisfying an inequality involving the average distance to the set of the system equilibria. These results are then used to develop semistable consensus protocols for discrete-time networks with communication uncertainty capturing measurement noise and attenuation errors in the information transfer between agents. The proposed distributed control architecture involves the exchange of information between agents guaranteeing that the closed-loop dynamical network is stochastically semistable to an equipartitioned equilibrium representing a state of almost sure consensus consistent with basic discrete-time thermodynamic principles.

机译：本文开发了Lyapunov和Converse Lyapunov定理，用于采用ITô型差分方程表示的离散时间随机半可爱的非线性动力系统，其具有均线连续尺度。具体而言，我们为随机半质植性提供必要和足够的Lyapunov条件，并表明随机半硅可用性意味着连续Lyapunov功能的存在，其差分运算符涉及无限时间的离散时间模拟用于连续时间ITO动态系统的离散时间模拟，并且沿着动态减少系统样本溶液序列满足涉及与系统均衡集合的平均距离的不等式。然后，这些结果用于开发用于离散时间网络的半可用共识协议，其中具有通信不确定性在代理之间的信息传输中捕获测量噪声和衰减误差。所提出的分布式控制架构涉及代理之间的信息交换，保证闭环动态网络随着与基本离散时间热力学原理一致的几乎肯定共识的状态而言，闭环动态网络是随机的均衡。

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《Mediterranean Conference on Control and Automation》|2021年|892-897|共6页
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Wassim M. Haddad; Junsoo Lee;
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Thermodynamics; Uncertainty; Stochastic systems; Measurement uncertainty; Tools; Nonlinear dynamical systems; Noise measurement;

机译：热力学;不确定性;随机系统;测量不确定性;工具;非线性动力系统;噪声测量;

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机译：通过传感器理论进行切换非线性系统的半峰值性和随机血丝性：应用于在随机网络中受约束分布式共识的应用
2. Stochastic Semistability for Nonlinear Dynamical Systems With Application to Consensus on Networks With Communication Uncertainty [J] . Haddad Wassim M., Rajpurohit Tanmay, Jin Xu IEEE Transactions on Automatic Control . 2020,第7期

机译：具有通信不确定性的网络与网络共识的非线性动力系统的随机血丝性
3. H_2 optimal semistable stabilisation for linear discrete-time dynamical systems with applications to network consensus [J] . Qing Hui, Wassim M. Haddad International Journal of Control . 2009,第3期

机译：线性离散时间动力系统的H_2最优半稳定镇定并应用于网络共识
4. H{sub}2 Optimal Semistable Stabilization for Linear Discrete-Time Dynamical Systems with Applications to Network Consensus [C] . Qing Hui, Wassim M. Haddad IEEE Conference on Decision and Control . 2007

机译：H {Sub} 2具有网络共识的应用程序与网络共识的线性离散时间动态系统的最佳半可稳定
5. Stochastic semistability with application to stochastic consensus. [D] . Zhou, Jing. 2011

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6. Nonuniform Exponential Dichotomies in Terms of Lyapunov Functions for Noninvertible Linear Discrete-Time Systems [O] . Ioan-Lucian Popa, Mihail Megan, Traian Ceauşu 2013

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7. DIGITAL CONTROL SYSTEMS IMPLEMENTATION TECHNIQUES, VOLUME 70 OF CONTROL AND DYNAMIC SYSTEMS: ADVANCES IN THEORY AND APPLICATIONS, C. Leondes (ed), Academic Press, San Diego, 1995, 390 pp., ISBN 0-12-0127702, $99.00 DISCRETE-TIME CONTROL SYSTEM ANALYSIS AND DESIGN, VOLUME 71 OF CONTROL AND DYNAMIC SYSTEMS: ADVANCES IN THEORY AND APPLICATIONS, C. Leondes (ed), Academic Press, San Diego, 1995, 410 pp., ISBN 0-12-0127715, $99.00 DISCRETE-TIME CONTROL SYSTEM IMPLEMENTATION TECHNIQUES, VOLUME 72 OF CONTROL AND DYNAMIC SYSTEMS: ADVANCES IN THEORY AND APPLICATIONS, C. Leondes (ed), Academic Press, San Diego, 1995, 388 pp., ISBN 0-12-0127725, $99.00 TECHNIQUES IN DISCRETE-TIME STOCHASTIC CONTROL SYSTEMS, VOLUME 73 OF CONTROL AND DYNAMIC SYSTEMS: ADVANCES IN THEORY AND APPLICATIONS, C. Leondes (ed), Academic Press, San Diego, 1995, 380 pp., ISBN 0-12-0127734, $99.00 TECHNIQUES IN DISCRETE AND CONTINUOUS ROBUST SYSTEMS, VOLUME 74 OF CONTROL AND DYNAMIC SYSTEMS: ADVANCES IN THEORY AND APPLICATIONS, C. Leondes (ed), Academic Press, San Diego, 1995, 412 pp., ISBN 0-12-0127741, $99.00 [O] . D. SUBBARAM NAIDU 1997

机译：数字控制系统的实施技术，控制和动态系统的第70卷：理论和应用的进步，C.丝丝（ED），学术出版社，圣地亚哥，1995,390 PP，ISBN 0-12-0127702，99.00美元离散时间控制系统分析和设计，控制和动态系统的第71卷：理论和应用的进步，C.丝丝（ED），学术出版社，圣地亚哥，1995,410 PP，ISBN 0-12-0127715，99.00美元离散时间控制系统实现技术，控制和动态系统的第72卷：理论和应用的进步，C.丝丝（ED），学术出版社，圣地亚哥，1995,388 pp，ISBN 0-12-0127725，99.00美元的离散 - 时间随机控制系统，控制和动态系统的VOLUME 73：前进，理论与应用，C Leondes（ED），学术出版社，圣地亚哥，1995年，380页，ISBN 0-12-0127734，在离散和$ 99.00技术。连续稳健的系统，控制和动态系统的第74卷：理论和应用的进步，C. leondes（ed），学术出版社，圣地亚哥，1995,412 pp。，ISBN 0-12-0127741，99.00美元

Lyapunov Theorems for Semistability of Discrete-Time Stochastic Systems with Application to Network Consensus with Random Communication Noise

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