Weighted‐average ℓ₁ filtering for switched positive systems

Abstract

Summary In this paper, the filtering problem for a class of switched positive systems with dwell time is investigated. A novel weighted‐average technique is proposed for filter design such that the final estimate of the unmeasurable outputs of the considered system is more accurate than that of traditional approaches. The main contributions of this paper are summarized as follows: By exploiting the positivity and characteristics of switched positive systems with dwell time, a candidate linear copositive Lyapunov function, which is both quasi‐time‐dependent and mode‐dependent, is presented to establish the closed‐loop stability of the considered systems. Upon the established closed‐loop stability, less conservative bounded positive filters (both upper‐bound and lower‐bound filter) with ℓ1 disturbance attenuation performance are designed for the considered system. By introducing a proper weight, a weighted‐average approach, which is more general than the bounded filter design method, is proposed for filter design. The worst ℓ1 disturbance attenuation performance of the novel developed filter is evaluated. Both the bounded filters and the weighted‐average filter are designed by solving standard linear programming problems. A numerical example illustrates the effectiveness of the proposed approach. Copyright © 2017 John Wiley & Sons, Ltd.

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.…”

“…This problem has been studied for a many systems including networked systems, T‐S fuzzy systems, positive linear systems, positive T‐S fuzzy systems, positive Markov jump systems, and switched systems . In addition, the works on filtering of switched positive systems are also not a few at present …”

“…40 In addition, the works on filtering of switched positive systems are also not a few at present. 26,[29][30][31]41 The works mentioned in the previous paragraph assume that the switching of the filter is always synchronous with that of the subsystem. However, there must exist a delay between the switching of the filter and the subsystem in practical systems.…”

Global exponential stability of 2D switched positive nonlinear systems described by the Roesser model

“…On the other hand, switched system including a series of subsystems and a switching signal is a class of hybrid systems . Much attention has been focused upon and some excellent research results on the theory of 1D switched positive systems have been published . Among these studies, stability analysis is one of the most important problem .…”

“…[14][15][16][17][18][19][20] Much attention has been focused upon and some excellent research results on the theory of 1D switched positive systems have been published. [21][22][23][24][25][26][27] Among these studies, stability analysis is one of the most important problem. 28,29 Recently, the stability theory of general switched systems is extended for 2D switched positive systems, which may occur in practical systems, such as in the thermal process with multiple modes.…”