Toward Stochastic Realization Theory for Generalized Linear Switched Systems With Inputs: Decomposition Into Stochastic and Deterministic Components and Existence and Uniqueness of Innovation Form

We study a class of stochastic Generalized Linear Switched System (GLSS), which includes subclasses of jump-Markov, piecewise-linear and Linear Parameter-Varying (LPV) systems. We prove that the output of such systems can be decomposed into deterministic and stochastic components. Using this decompo...

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Bibliographic Details
Published in:IEEE control systems letters 2024-01, Vol.8, p.1841-1846
Main Authors: Rouphael, Elie, Mejari, Manas, Petreczky, Mihaly, Belkoura, Lotfi
Format: Article
Language:English
Subjects:
Automatic
Engineering Sciences
innovation representation
Linear systems
Stochastic processes
stochastic realization theory
Switched systems
Switches
System identification
Technological innovation
White noise
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Summary:We study a class of stochastic Generalized Linear Switched System (GLSS), which includes subclasses of jump-Markov, piecewise-linear and Linear Parameter-Varying (LPV) systems. We prove that the output of such systems can be decomposed into deterministic and stochastic components. Using this decomposition, we show existence of state-space representation in innovation form, and we provide sufficient conditions for such representations to be minimal and unique up to isomorphism.
ISSN:2475-1456
2475-1456
DOI:10.1109/LCSYS.2024.3417189