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Uniform global controllability of a linear system with stationary random parameters. (English. Russian original) Zbl 0795.93013

Differ. Equations 27, No. 11, 1289-1295 (1991); translation from Differ. Uravn. 27, No. 11, 1843-1850 (1991).
Summary: This is an investigation of the uniform global controllability of the system \[ \dot x= A(t,\omega)x+ B(t,\omega)u,\quad \omega\in \Omega, \] to zero, with a given probability, where \(x\) is the \(n\)-phase vector, \(u\) is the \(m\)-dimensional control, and \(A\) and \(B\) are random matrices.
Global and uniform global controllability of a system in the determinate case are investigated by E. L. Tonkov [ibid. 19, No. 2, 269-278 (1983; Zbl 0528.93017)]. In the present work some of the results of this theory are extended to apply to systems with stationary random parameters. Such problems arise in various practical cases in the investigation of systems subjected to random perturbations.

MSC:

93B05 Controllability
93C15 Control/observation systems governed by ordinary differential equations
93C73 Perturbations in control/observation systems

Citations:

Zbl 0528.93017
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