Fundamental Bounds for Stabilizability of Continuous-Time Systems under Stochastic Multiplicative Uncertainty and Delay*

This paper is devoted to stabilization problem of linear time-invariant (LTI) continuous-time systems under stochastic multiplicalive uncertainty and time-delay. In its full generality, we model the stochastic multiplicative uncertainty as a random process with a certain distribution. We assess the stability of system based on mean-square criteria. Our main contribution includes the fundamental condition, both necessary and sufficient, which insures that the single-input single-output systems (SISO) can be mean-square stabilized by output feedback. This condition provides explicitly a fundamental limit on mean-square staibilizability imposed by the signal-to-noise ratio (SNR), the system’s unstable poles, nonminimum phase zeros and time-delay.