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Mean square stabilization of linear systems by mean zero noise
Stochastics and Stochastic Reports, 1999A necessary and sufficient condition for the mean square stabilization of time-varying linear systems of ordinary differential equations by zero mean real noise is obtained.
Roman V. Bobryk, Lukasz Stettner
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On the Mean Square Stability of Random Linear Systems
IRE Transactions on Circuit Theory, 1959The theory of random linear systems is extended to systems containing one or more non-independent parameters under the assumption that the parameter processes and the solution process have very widely separated spectra. It is shown that the second product moment of the solution satisfies a linear integral equation which can be solved in closed form in ...
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Mean-square Stabilization of Invariant Manifolds for SDEs
IFAC Proceedings Volumes, 2014Abstract We consider systems of Ito's stochastic differential equations with smooth compact invariant manifolds. The problem addressed is an exponential mean square (EMS) stabilization of these manifolds. The necessary and sufficient conditions of the stabilizability are derived on the base of the spectral criterion of the EMS-stability of invariant ...
Lev Ryashko, Irina Bashkirtseva
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Journal of the Franklin Institute, 2018
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Zhiguo Yan, Yunxia Song, Ju H. Park 0001
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Zhiguo Yan, Yunxia Song, Ju H. Park 0001
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Mean square exponential stability of stochastic nonlinear delay systems
International Journal of Control, 2016ABSTRACTIn this paper, we are concerned with the stability of stochastic nonlinear delay systems. Different from the previous literature, we aim to show that when the determinate nonlinear delay system is globally exponentially stable, the corresponding stochastic nonlinear delay system can be mean square globally exponentially stable.
Quanxin Zhu, Shiyun Song, Tianren Tang
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On mean-square optimum stabilization at damped random perturbatios
Journal of Applied Mathematics and Mechanics, 1961Die Aufgabe der Bestimmung eines optimalen Reglers in einem linearen System mit abklingender zufälliger Störung wird mit Hilfe der Methode der Lyapunovschen Funktionen und Prinzipien der dynamischen Programmierung behandelt. Dabei wird als Optimalitätskriterium gefordert, daß das Integral über den mittleren quadratischen Fehler minimal ist.
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Mean square stabilization control of switched systems with stochastic disturbances
2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601), 2004In this paper, the mean square (MS) stability and exponential mean square (EMS) stability of multivariable switched stochastic systems are investigated. Based on the concept of the average dwell-time and the ratio of the total time running on all unstable subsystems to the total time running on all stable subsystems, some sufficient conditions are ...
Wei Feng, Ji-Feng Zhang
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Mean square stability for Kalman filtering with Markovian packet losses
Automatica, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Keyou You +2 more
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On the mean square stability of linear difference equations
Applied Mathematics and Computation, 1979The mean square asymptotic stability of linear stochastic difference equations is studied. The Liapunov method of stability analysis is extended to stochastic difference equations, and several criteria for the mean square stability of the equilibrium state are established. Two examples of the application of the stability theorems are also considered.
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