arXiv subjects

Elie Rouphael

Publications and source records attributed to Elie Rouphael.

3 recordsLinked to original sources

arXiv2024

Minimal covariance realization and system identification algorithm for a class of stochastic linear switched systems with i.i.d. switching

In this paper, we consider stochastic realization theory of Linear Switched Systems (LSS) with i.i.d. switching. We characterize minimality of stochastic LSSs and show existence and uniqueness (up to isomorphism) of minimal LSSs in innovation form. We present a realization algorithm to compute a minimal LSS in innovation form from output and input covariances. Finally, based on this realization algorithm, by replacing true covariances with empirical ones, we propose a statistically consistent system identification algorithm.

math.OC↗

arXiv2024

Towards stochastic realization theory for Generalized Linear Switched Systems with inputs: decomposition into stochastic and deterministic components and existence and uniqueness of innovation form

In this paper, we study a class of stochastic Generalized Linear Switched System (GLSS), which includes subclasses of jump-Markov, piecewide-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.

math.OC↗

arXiv2022

On minimal LPV state-space representations in innovation form: an algebraic characterization

In this paper we will propose a definition of the concept of minimal state-space representations in innovation form for LPV. We also present algebraic conditions for a stochastic LPV state-space representation to be minimal in forward innovation form and discuss an algorithm for transforming any stochastic LPV state-space representation to a minimal one in innovation form.

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