Projection-based degree of distinguishability in switching linear systems

Abstract

In this paper, we consider the problem of identifying the active mode of a switching linear system from data sequences of a finite length. The results combine elements from canonical correlation analysis and subspace projection methods. In addition to providing insight into the geometric meaning of the problem, the results turn out to be of practical relevance whenever mode identification is addressed in the presence of noisy-corrupted measurements. In particular, the results can be used to provide a characterization of the regions of the space where mode identification occurs independently of a prescribed noise level

Model-Based Modes Detection and Discernibility for Switched Affine Discrete-Time Systems

“…That corroborates the non reversibility of the discernibility as highlighted by Proposition 12. Let us notice that a close notion has been introduced in [27], [28] under the name degree of distinguishability at x and is suitable to cope with noisy measurements. The notion combines elements from canonical correlation analysis and subspace projection methods.…”

“…That may cause the estimation of the sequence σs as in Proposition 10 or even worse the estimation of the active mode σ * (k) as in Corollary 3 to be unsuccessful since the uniqueness is not satisfied. Next section is devoted to the solutions that allow to circumvent such a point, the horizon length being kept unchanged, that is h still verifying (27).…”