Mean square stabilization of linear systems by mean zero noise

A 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. The noise sources are generated either by Ornstein-Uhlenbek process or telegraphic process

[1]  Ł. Stettner,et al.  Stabilization of two-dimensional linear systems by Gaussian noise , 1998 .

[2]  N. Sri Namachchivaya,et al.  Small Noise Expansion of Moment Lyapunov Exponents for Two-Dimensional Systems , 1997 .

[3]  L. Arnold,et al.  Large noise asymptotics of invariant measures, with applications to Lyapunov exponents , 1996 .

[4]  N. Sri Namachchivaya,et al.  Moment Lyapunov Exponent for Two Coupled Oscillators Driven by Real Noise , 1996, SIAM J. Appl. Math..

[5]  Xuerong Mao,et al.  Stochastic stabilization and destabilization , 1994 .

[6]  V. Wihstutz,et al.  Stabilization of companion form systems by mean zero noise , 1994 .

[7]  L. Arnold Stabilization by Noise Revisited , 1990 .

[8]  Bruce E. Hajek,et al.  Review of 'Approximation and Weak Convergence Methods for Random Processes, with Applications to Stochastic Systems Theory' (Kushner, H.J.; 1984) , 1985, IEEE Transactions on Information Theory.

[9]  Hans Crauel,et al.  Stabilization of Linear Systems by Noise , 1983 .

[10]  R. Khasminskii Stochastic Stability of Differential Equations , 1980 .

[11]  I. Olkin,et al.  Inequalities: Theory of Majorization and Its Applications , 1980 .

[12]  M. Kreĭn,et al.  Stability of Solutions of Differential Equations in Banach Spaces , 1974 .

[13]  U. Frisch,et al.  Solving linear stochastic differential equations , 1974 .

[14]  U. Frisch,et al.  Brownian motion of harmonic oscillator with stochastic frequency , 1973 .

[15]  R. Khas'minskii,et al.  Stability of a linear system with random disturbances of its parameters , 1967 .

[16]  Martin A. Leibowitz,et al.  Statistical Behavior of Linear Systems with Randomly Varying Parameters , 1963 .

[17]  F. Kozin,et al.  Moments of the Output of Linear Random Systems , 1962 .

[18]  Thomas K. Caughey,et al.  Comments on “On the Stability of Random Systems” , 1960 .

[19]  J. Clifton Samuels,et al.  On the Stability of Random Systems and the Stabilization of Deterministic Systems with Random Noise , 1960 .