Stabilization of Networked Delay Systems
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In this chapter, we study the stabilization of networked feedback systems in the presence of stochastic uncertainties and time delays. We model the stochastic uncertainty as a random process in a multiplicative form, and we assess the stability of system based on mean-square criteria. Based on the mean-square small-gain theorem, Theorem 2.5, we develop fundamental conditions of mean-square stabilizability, which ensure that an open-loop unstable system can be stabilized by output feedback. For SISO systems, a general, explicit stabilizability condition is obtained. This condition, both necessary and sufficient, provides a fundamental limit imposed by the system’s unstable poles, nonminimum phase zeros, and time delay. This condition answers to the question: What is the exact largest range of delay such that there exists an output feedback controller mean-square stabilizing all plants under a stochastic multiplicative uncertainty for delays within that range? For MIMO systems, we provide a solution for minimum phase systems possibly containing time delays, in the form of a generalized eigenvalue problem. Limiting cases are also showing how the directions of unstable poles may affect mean-square stabilizability of MIMO minimum phase systems.