Distinguishability of discrete‐time linear systems

Abstract

This article introduces the notion of absolutely distinguishable discrete‐time dynamic systems, with particular applicability to linear time‐invariant and linear parameter‐varying systems. The motivation for this novel type of distinguishability stems, in particular, from the stability and performance requirements of worst‐case adaptive control methodologies. The main results presented herein show that, in most practical cases, a persistence of excitation type of condition and a minimum number of iterations are required to properly distinguish two dynamic systems. We also demonstrate that the former constraint can be written as a lower bound on the intensity of the exogenous disturbances. The applicability of the developed theory is illustrated with a set of examples.

Set-valued estimators for Uncertain Linear Parameter-Varying systems

“…Notice that Problem 1 is called state estimation although a converse definition could be presented for the output of the system (this is of particular interest in sensitivity analysis (Silvestre et al (2019)) and system distinguishability (Silvestre et al (2021))).…”

Minimax Adaptive Estimation for Finite Sets of Linear Systems

“… Silvestre et al,[21], recently reexamined the distinguishability requirements from a multiple-model adaptive control perspective.…”