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Mean-Square Stability and Stabilizability for LTI and Stochastic Systems Connected in Feedback
- Publication Year :
- 2024
-
Abstract
- In this paper, the feedback stabilization of a linear time-invariant (LTI) multiple-input multiple-output (MIMO) system cascaded by a linear stochastic system is studied in the mean-square sense. Here, the linear stochastic system can model a class of correlated stochastic uncertainties such as channel uncertainties induced by packet loss and random transmission delays in networked systems. By proposing a key parameter called coefficient of frequency variation to characterize the correlation of the stochastic uncertainties, we present a necessary and sufficient condition of the mean-square stability for this MIMO stochastic feedback system. After then a necessary and sufficient condition for the mean-square stabilizability is provided, which reveals a fundamental limit imposed by the system's unstable poles, nonminimum-phase (NMP) zeros, relative degrees (input delays), and the coefficient of frequency variation of the stochastic uncertainties. A numerical example is presented to illustrate the fundamental constraints in the mean-square stabilizability of MIMO networked systems with parallel communication channels.
- Subjects :
- Electrical Engineering and Systems Science - Systems and Control
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2402.04074
- Document Type :
- Working Paper