Non‐minimum phase switched systems: HOSM‐based fault detection and fault identification via Volterra integral equation

Abstract

In this paper, the problem of continuous and discrete state estimation for a class of linear switched systems with additive faults is studied. The class of systems under study can contain non-minimum phase zeroes in some of their 'operating modes'. The conditions for exact reconstruction of the discrete state are given using structural properties of the switched system. The state space is decomposed into the strongly observable part, the non-strongly observable part, and the unobservable part, to analyze the effect of the unknown inputs. State observers based on high-order sliding mode to exactly estimate the strongly observable part and Luenberger-like observers to estimate the remaining parts are proposed. For the case when the exact estimation of the state cannot be achieved, the ultimate bounds on the estimation errors are provided. The proposed strategy includes a high-order sliding-mode-based fault detection and a fault identification scheme via the solution of a Volterra integral equation. The feasibility of the proposed method is illustrated by simulations.

State estimation for linear hybrid systems with periodic jumps and unknown inputs

“…For the sake of clarity and without loss of generality, it is assumed that , that is, p =1. However, under some mild conditions, the multiple‐output multiple‐unknown input case can be designed straightforwardly following the ideas given in Reference .…”

Fault detection based on higher‐order sliding mode observer for a class of switched linear systems

“…Following [19], let us introduce vector k defined in (18) where q,k is such that ∀k ≥ η + 1, ∀q = k − η, . .…”

Continuous and discrete state estimation for switched LPV systems using parameter identification

“…The reverse procedure can also be applied, i.e. discrete state estimation based on the continuous state information, as it is described by [19] and [21], based on sliding mode observers. In [27] necessary and sufficient conditions for a linear switched systems to be invertible are proposed, i.e.…”