Positive $$L_1 $$ L 1 Observer Design for Positive Switched Systems

Abstract

This paper investigates the problem of L 1 observer design for positive switched systems. Firstly, a new kind of positive L 1 observer is proposed for positive switched linear delay-free systems with observable and unobservable subsystems. Based on the average dwell time approach, a sufficient condition is proposed to ensure the existence of the positive L 1 observer. Under the condition obtained, the estimated error converges to zero exponentially, and the L 1 -gain from the disturbance input to the estimated error is less than a prescribed level. Then the proposed design result is extended to positive switched systems with mixed time-varying delays, where the mixed time-varying delays are presented in the form of discrete delay and distributed delay. Finally, two numerical examples are given to demonstrate the feasibility of the obtained results.

Observers design for switched discrete-time singular time-delay systems with unknown inputs

“…However, the decay rate 1 1−α of the resulting observation error systems is a monotonic increasing function on the parameter α. Thus, we can first select a small initial value of α such that (16) and (33) may have a feasible solution, then increase α step by step to obtain a larger decay rate so as to speed the convergence of the observation error without destroying the feasibility of inequalities (16) and (33).…”

“…In Theorems 1 and 2, α is a given parameter, and the feasibility of LMIs (16) and (33) depends on the selection of α. The smaller α is, the better feasibility of (16) and (33) is.…”

“…The smaller α is, the better feasibility of (16) and (33) is. However, the decay rate 1 1−α of the resulting observation error systems is a monotonic increasing function on the parameter α.…”

“…On the other hand, time delays are the inherent features of many physical process and often a source of instability and poor performances. Since 1990s, switched systems with or without time delays have been extensively studied, and many useful results on observability and Luenberger-type observer design have been reported; see [11][12][13][14][15][16][17][18][19] and the references therein. However, few efforts are devoted to design observers for switched systems with UIs.…”

A novel approach to L1 filter design for asynchronously switched positive linear systems with dwell time

“…Many results on the L 1 ‐gain analysis and synthesis problems of switched positive systems have been obtained. To mention a few, the L 1 ‐gain performance of switched positive singular systems with delays has been studied in the work of Li and Lin, the stability and L 1 ‐gain performance of switched positive linear systems (SPLSs) have been studied in the work of Xiang et al, and the robust stability and L 1 ‐gain performance of switched positive fuzzy systems have been investigated in the work of Li et al The readers can refer to the literature for further results.…”