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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 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 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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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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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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Stability in mean square of a linear stochastic differential equation
Journal of Soviet Mathematics, 1993See the review in Zbl 0674.60065.
Valeev, K. G., Sulima, I. M.
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Mean-square stability of the Normalized Least-Mean Fourth algorithm for white Gaussian inputs
Digital Signal Processing, 2011Normalized forms of adaptive algorithms are usually sought in order to obtain convergence properties independent of the input signal power. Such is the case of the well-known Normalized LMS (NLMS) algorithm. The Least-Mean Fourth (LMF) adaptive algorithm has been shown to outperform LMS in different situations.
Neil J. Bershad +1 more
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Exponential mean-square stability of stochastic string hybrid systems
2009 European Control Conference (ECC), 2009The sufficient conditions of exponential mean-square stability for nonlinear continuous time stochastic string hybrid systems are established. The excitations are assumed to be parametric white noises and the switching rule has the form of a right continuous Markov chain. The detailed calculations are given for linear systems.
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