STABILITY OF LINEAR SYSTEMS WITH MARKOVIAN JUMPS
DOI:
https://doi.org/10.17268/sel.mat.2016.02.03Keywords:
Linear systems with Markov jumps, stability, Markov chainsAbstract
In this work we will analyze the stability of linear systems governed by a Markov chain, this family is known in the specialized literature as linear systems with Markov jumps or by its acronyms in English MJLS as it is denoted in [1]. Linear systems governed by a Markov chain are dynamic systems with abrupt changes. We give some denitions of stability for the MJLS system, where these types of stability are equivalent as long as the state space of the Markov chain is finite.
Finally we present a theorem that characterizes the stochastic stability by means of an equation of the Lyapunov type. The result is a generalization of a theorem in classical theory.
References
Costa, Oswaldo Luiz do Valle. Discrete-time Markov jump linear systems Springer, London, 2005.
B. L. Stevens and F.L. Lewis Aircraft Modeling, Dynamics and Control , New York, NY: Wiley (1991).
R.W. Newcomb The Semistate Description of Nonlinear Time-Variable Circuits,, IEEE Trans. Autom. Control Vol CAS-28 No.1, January (1981) pp.62-71.
Yuandong Ji. Chizeck Howard. Jump Linear Quadratic gaussian control: Steady-State Solution and Testable Conditions, Control-Theory and Advanced Technology Vol 6. No.3, (1990) pp.289-319.
Tejada R. Arturo. Analysis of error recovery eects on digital flight control systems. Ms Dissertation, Old Dominion University 2002.
Feng Xiangbo. Loparo Kenneth. & Yuandong Ji. Chizeck Howard. Stochastic Stability properties of Jump Linear Systems,IEEE Transactions on Automatic Control, vol 37 No.1, 1992 pp. 38-53.
Fang, Y. Stability analysis of linear control systems with uncertain parameters , Ph.D. Dissertation, Dept. of Systems, Control, and Industrial Engineering, Case Western Reserve University, Cleveland, OH.Springer, London, 1998.
Mayta G. Jorge. Regularidad y Estabilidad de Sistemas Lineales con Saltos Markovianos en Tiempo Discreto. Tesis M.S, Dpto. Matematica, Ponticia Universidad Catolica del Peru, Lima, Peru 2015.
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