Mixed l −/l 1 fault detection observer design for positive switched systems with time-varying delay via delta operator approach

Abstract

This paper investigates the problem of fault detection observer design for positive switched systems with time-varying delay via delta operator approach. A new fault sensitivity measure, called lindex, is proposed. The l -fault detection observer design and multi-objective l -/l 1 fault detection observer design problems are addressed. Based on the average dwell time approach and the piecewise copositive type Lyapunov-Krasovskii functional method in delta domain, sufficient conditions for the existence of such two kinds of fault detection observers are firstly given, and then the design methods are presented. Finally, two examples are provided to show the effectiveness and the applicability of the proposed methods.

Fault detection for switched positive systems under successive packet dropouts with application to the Leslie matrix model

“…On the other hand, the L performance represents a measure for the fault sensitivity of the switched positive system, which is parallel to the H performance index in the non-positive systems. As a mixed performance index, H =H 1 has been proposed to deal with the fault detection problem for non-positive systems in [18] and, similarly, a mixed performance L =L 1 has been established to such a problem in the continuous time switched positive systems [17]. The present paper aims at solving such problem in the discrete time switched positive systems.…”

“…well as parameter uncertainties. Accordingly, some relevant results have been reported [11,17,18], where the main idea is to transform the FD problem into an H =H 1 or H 1 filtering problem [15,[18][19][20]. This idea has recently been extended to switched positive systems.…”

“…This idea has recently been extended to switched positive systems. For example, an L 1filtering design problem for a continuous-time switched positive delay system has been studied in [16], and the fault detection of positive switched systems with time-varying delay has been achieved by designing a mixed L =L 1 observer via the delta operator approach in [17].On the other hand, in the transmission and processing of measurement data from the sensors to the filter/estimator/detector, the packet dropout (or missing measurements) is usually unavoidable due mainly to the limited bandwidth of the channels and temporal sensor failures. Clearly, the packet dropout would degrade the system performance, and its impact on the fault detection problem has been an emerging challenging problem [21].…”

“…This idea has recently been extended to switched positive systems. For example, an L 1filtering design problem for a continuous-time switched positive delay system has been studied in [16], and the fault detection of positive switched systems with time-varying delay has been achieved by designing a mixed L =L 1 observer via the delta operator approach in [17].…”

Finite-time H ∞ control for switched systems with time-varying delay using delta operator approach

“…In [19], robust stabilization problem for discrete-time systems with time-varying delays was discussed. Some results on filter and observer design of delta operate systems were obtained in [20,21]. It should be pointed out that the aforementioned results are on Lyapunov stability.…”