Conditions for distinguishability and observability of switched linear systems

Projection-based degree of distinguishability in switching linear systems

“…except when no motion occurs. In the literature on switching linear systems, this case is usually referred to as to mode-observable case, so as to indicate the possibility of reconstructing the mode of the systems whenever its initial state is different from zero [8], [25], [16]. Theorem 2 extends such an analysis in a quite natural way, providing a characterization of distinguishability in terms of distance from the set of initial states where π q ′ (O q x) = 0.…”

“…In the literature, linear systems have been mainly addressed ( [8]- [16]). Most of the attention has been devoted to date to the only question of whether or not two systems are distinguishable, with no tools for quantifying how far from (or close to) indistinguishability two systems are.…”

Observability and Observer Design for Continuous-Time Perturbed Switched Linear Systems under Unknown Switchings

“…Let P0 be a projection matrix such that ker P0 = Im (Y0S). Thus Let then (17) and (18) can be combined to get q1 (t) ^x ( t ) . It is easy to see that ker Y0 ٨ ker( Po٢٨٨) K n A -1(K + ‫.…”

“…This is usually referred to as the distinguishability problem. This problem, together with the SLS observability, has been extensively studied in the literature for the case of known in puts [1,9,13,18,20]. However, the observability of continuous-time SLS subject to unknown dis turbances and unknown switching signals has re ceived less attention.…”

Mode discernibility and bounded-error state estimation for nonlinear hybrid systems

“…Therefore, the main ingredient of our SME for hybrid systems is the ability to distinguish the current active location mode from the observation of the input-output behaviour. To the best of our knowledge, the observability and detectability of hybrid systems have been studied only for linear switching systems (Babaali and Pappas, 2005;De Santis et al, 2003Fliess et al, 2008;De Santis, 2011;De Santis and Di Benedetto, 2017;Lou and Yang, 2011). In this paper we introduce a new computable condition for analyzing mode discernibility for the general class of nonlinear hybrid systems.…”