Jie Chen (City University of Hong Kong)
Quantized Control under Multiplicative Noise: Fundamental Conditions of Stabilizability
Quantized channels with random multiplicative noises have found wide utilities in modeling networked control systems subject to, e.g., packet drops, random delays, and fading. In this talk I shall present some of our recent results on stabilization and optimal control of networked feedback systems with communication links modeled as such quantized channels with quantization errors and transmission imperfections described by random multiplicative noises. A particular emphasis will be the development of fundamental conditions of mean square stabilizability which insure that an open-loop unstable system can be stabilized via quantized feedback in the mean square sense. For single-input single-output systems, a general, explicit stabilizability condition is obtained, which provides a fundamental limit on the channel noise variance imposed by the system’s unstable poles, nonminimum phase zeros and time delay. For multi-input multi-output systems, we provide a complete, computationally efficient solution for minimum phase systems possibly containing time delays, construed as the solution to a generalized eigenvalue problem readily solvable by means of linear matrix inequality optimization. Limiting cases and nonminimum phase plants are analyzed in further depth for conceptual insights, with an emphasis on how the directions of unstable poles and nonminimum phase zeros may affect mean square stabilizability in MIMO systems.