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Stability and disturbance attenuation for a switched Markov jump linear system [article]

Collin C. Lutz, Daniel J. Stilwell
2014 arXiv   pre-print
We address a class of Markov jump linear systems that are characterized by the underlying Markov process being time-inhomogeneous with a priori unknown transition probabilities.  ...  In both cases, conditions are expressed as a set of finite-dimensional linear matrix inequalities that can be solved efficiently.  ...  We address a switched Markov jump linear system, which is simply a time-inhomogeneous Markov jump linear system where the underlying Markov chain is characterized by an a priori unknown sequence of transition  ... 
arXiv:1411.5923v1 fatcat:cwqtxfgvjjcs7c3mimgma65cqy

Stochastic stability of jump linear systems

Yuguang Fang, K.A. Loparo
2002 IEEE Transactions on Automatic Control  
., second moment) stability for discrete-time jump linear systems with timehomogenous and time-inhomogenous finite state Markov chain form processes are presented.  ...  INTRODUCTION In this note, second moment (mean square) stability for the jump linear system (1.1) whose form process f k g is a finite state time-homogenous or time-inhomogenous Markov chain is studied  ...  The system is modeled as a jump linear system with an inhomogenous Markov chain and they obtained a necessary and sufficient condition for exponential stability.  ... 
doi:10.1109/tac.2002.800674 fatcat:nfbhqy47hbbhxl2q7qc4ak7agi

Stability Analysis of Stochastic Hybrid Jump Linear Systems Using a Markov Kernel Approach

Arturo Tejada, Oscar R. Gonzalez, W. Steven Gray
2013 IEEE Transactions on Automatic Control  
Index Terms-Finite state machine (FSM), hybrid systems, Markov chains, Markov jump systems, Markov kernel, mean square stability, stochastic systems.  ...  For this class of hybrid jump linear systems, the switching signal is, in general, a non-Markovian process, making it hard to analyze its stability properties.  ...  computer faults, and a Markov jump linear system driven by an inhomogeneous Markov chain.  ... 
doi:10.1109/tac.2013.2275665 fatcat:ag2rmcor4nhujnos262yzl73z4

Linear quadratic regulation of polytopic time-inhomogeneous Markov jump linear systems (extended version) [article]

Y. Zacchia Lun, A. Abate, A. D'Innocenzo
2019 arXiv   pre-print
In most real cases transition probabilities between operational modes of Markov jump linear systems cannot be computed exactly and are time-varying.  ...  We take into account this aspect by considering Markov jump linear systems where the underlying Markov chain is polytopic and time-inhomogeneous, i.e. its transition probability matrix is varying over  ...  INTRODUCTION In discrete-time Markov jump linear systems (MJLSs), the transition probabilities of jumps between operational modes are fundamental in determining the dynamic behaviour [1] .  ... 
arXiv:1903.03091v1 fatcat:j64eudp7dvhplj6ik2dmz4o3au

Page 4073 of Mathematical Reviews Vol. , Issue 85i [page]

1985 Mathematical Reviews  
4073 Loparo, Kenneth A. (1-CWR-E) 85i:60055 Stochastic stability of coupled linear systems: a survey of methods and results. Stochastic Anal. Appl. 2 (1984), no. 2, 193-228.  ...  In this paper we investigate the almost-sure stability properties of the sample-trajectories of linear stochastic systems with parametric excitation.” G. Papanicolaou (New York) Roerdink, J. B. T. M.  ... 

2020 Index IEEE Transactions on Automatic Control Vol. 65

2020 IEEE Transactions on Automatic Control  
., +, TAC Dec. 2020 5384-5391 Stability Analysis of Discrete-Time Semi-Markov Jump Linear Systems.  ...  ., +, TAC Oct. 2020 4005-4015 Control of Continuous-Time Linear Systems With Markov Jump Parameters in Reverse Time.  ...  Linear programming A Decentralized Event-Based Approach for Robust Model Predictive Control.  ... 
doi:10.1109/tac.2020.3046985 fatcat:hfiqhyr7sffqtewdmcwzsrugva

Page 1114 of Mathematical Reviews Vol. , Issue 84c [page]

1984 Mathematical Reviews  
Furthermore, under certain restrictions on the Lyapunov functional constructed, the linear stochastic delay differential systems and the stability property of corresponding unperturbed linear deterministic  ...  functions to study the usual stability property of sample orbits of solutions of relatively general time-inhomogeneous stochastic Ité differential equations with respect to the origin.  ... 

Page 1894 of Mathematical Reviews Vol. 56, Issue 5 [page]

1978 Mathematical Reviews  
Author’s summary: “For the linearized Boltzmann equation with finite cross section, the solution is represented as an integral over the paths of a Markov jump process.  ...  The author proves that Onsager’s reciprocal relations follow directly from the Master equation for a time reversal invariant Markov system.  ... 

An introduction to probabilistic methods with applications

Pierre Del Moral, Nicolas G. Hadjiconstantinou
2010 Mathematical Modelling and Numerical Analysis  
This special volume of the ESAIM Journal, Mathematical Modelling and Numerical Analysis, contains a collection of articles on probabilistic interpretations of some classes of nonlinear integrodifferential  ...  of applications.  ...  The preparation of this special volume was a joint effort by a number of people. We are very grateful to the Chief Editors of the journal, C. Le Bris and A.T.  ... 
doi:10.1051/m2an/2010043 fatcat:4x6toxjonbghfhzvjtzld562ri

Complex Boundary Value Problems of Nonlinear Differential Equations: Theory, Computational Methods, and Applications

Xinguang Zhang, Yong Hong Wu, Dragoş-Pătru Covei, Xinan Hao
2013 Abstract and Applied Analysis  
Acknowledgment Here, we would like to thank all the authors and reviewers of the papers for their excellent contributions. Xinguang Zhang Yong Hong Wu Dragos ¸-Pȃtru Covei Xinan Hao  ...  In the paper titled "h-Stability of linear matrix differential systems, " the authors investigate the stability problem of linear matrix differential systems by employing the Kronecker product of matrices  ...  boundary problems on time scale.  ... 
doi:10.1155/2013/705482 fatcat:hkwxefx2rfb73nfflmypdcp3ya

Page 4990 of Mathematical Reviews Vol. , Issue 95h [page]

1995 Mathematical Reviews  
The inhomogeneity gradually grows: a region of the inhomogeneous space violently oscillates in time and another region expands fast.  ...  In other words, the inhomogeneity, the oscillation, and the de- crease behaviour of the curvature are closely related to stability and orderliness of the correlated system.” 95h:82034 82C70 47D06 47NS55  ... 

Page 468 of Mathematical Reviews Vol. 58, Issue 1 [page]

1979 Mathematical Reviews  
A.; Kalzanov, K. 58 #3092 An estimate of the stability of a queueing system. (Russian) Taskent. Gos. Univ. Nauén. Trudy Vyp. 490 Voprosy Matematiki (1976), 21-26, 260.  ...  Dimitrov (Sofia) Do Le Minh 58 +3098 The discrete-time single-server queue with time-inhomogeneous compound Poisson input and general service time distribution. J. Appl.  ... 

Mathematical Approaches in Advanced Control Theories

Baocang Ding, Lihua Xie, Weihai Zhang, Xianxia Zhang, Qiang Ling, Yugeng Xi
2012 Journal of Applied Mathematics  
The designed controller can robustly guarantee stability and performance. Q. Ling and H. Deng study the second moment stability of a Markov jump linear system with real states.  ...  Pan investigate the problem of robust stability of uncertain linear discrete-time system over network with bounded packet loss. X.  ... 
doi:10.1155/2012/984296 fatcat:xommhyimknf2nekfqcda6r4k6e

Author index volume 38 (1991)

1991 Stochastic Processes and their Applications  
., On the product of two harmonizable time series El Karoui, N. and S.  ...  Runggaldier, On diffusion approximations for filtering Liu, X., Infinite reversible nearest particle systems in inhomogeneous and random environments * The issue number is given in front of page numbers  ... 
doi:10.1016/0304-4149(91)90101-h fatcat:jjtruehbmfen7gs4s3k2nkv3em

A Probabilistic Characterization of Random and Malicious Communication Failures in Multi-Hop Networked Control [article]

Ahmet Cetinkaya, Hideaki Ishii, Tomohisa Hayakawa
2018 arXiv   pre-print
The control problem of a linear discrete-time dynamical system over a multi-hop network is explored.  ...  We obtain a sufficient condition for the stability of the networked control system by utilizing our probabilistic approach.  ...  Di Beneditto, M., “On stability of time-inhomogeneous markov jump linear systems,” in Proc. IEEE Conf. Dec. Contr., pp. 5527–5532, 2016.  ... 
arXiv:1711.06855v3 fatcat:kraef7mnfvhfbj5heg4hlray3q
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