Weighted-average ℓ₁ filtering for switched positive systems

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.