Stochastic stabilization of linear systems under delayed and noisy feedback control

This paper is to study the stabilizability and stabilization issues of linear dynamical systems based on the delayed and noisy feedback control. For the general linear systems, the necessary conditions and sufficient conditions for mean square and almost sure stabilizability are deduced and the corresponding feedback controls are designed according to the generalized algebraic Riccati equation. It is revealed that the stabilizability is up to the system parameters (delays, noises, and unstable eigenvalues of the original system) and unstable systems can be stabilized in mean square if the feedback control is disturbed by noises with small intensities. It is showed that second-order integrator systems must be stabilizable for any given noise intensity and delay.