Finite-time Stability Analysis of Switched Linear Singular Systems

Xia, Biao; Lian, Jie; Shao, Cheng; Shi, Peng

doi:10.3182/20140824-6-za-1003.01877

Cited by 4 publications

(4 citation statements)

References 33 publications

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“…Then the observability of the switched system does not depend on k s . In fact, the observability condition (13) can be reduced to…”

Section: B Large Enough Observation Timementioning

confidence: 99%

“…In the continuous time domain, SLSSs have been studied extensively. The solvability issue is well established in [10], [11] while the stability issue is comprehensively studied in [10], [12], [13], [14]. Furthermore, the controllability and observability characterizations are satisfactorily formulated in [15], [16], [17], and some strategies are already developed to control such systems (see e.g.…”

Section: Introductionmentioning

confidence: 99%

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Observability of Singular Linear Switched Systems in Discrete Time: Single Switch Case

Sutrisno

Trenn

2021

2021 European Control Conference (ECC)

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In this paper, we investigate the observability of singular linear switched systems in discrete time. As a preliminary study, we restrict ourselves to systems with a single switch switching signal, i.e. the system switches from one mode to another mode at a certain switching time. We provide two necessary and sufficient conditions for the observability characterization. The first condition is applied for arbitrary switching time and the second one is for switching times that are far enough from the initial time and the final time of observation. These two conditions explicitly contain the switching time variable that indicates that in general, the observability is dependent on the switching time. However, under some sufficient conditions we provide, the observability will not depend on the switching time anymore. Furthermore, the observability of systems with two-dimensional states is independent of the switching time. In addition, from the example we discussed, an observable switched system can be built from two unobservable modes and different mode sequences may produce different observability property; in particular, swapping the mode sequence may destroy observability.

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“…Then the observability of the switched system does not depend on k s . In fact, the observability condition (13) can be reduced to…”

Section: B Large Enough Observation Timementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Observability of Singular Linear Switched Systems in Discrete Time: Single Switch Case

Sutrisno

Trenn

2021

2021 European Control Conference (ECC)

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“…This is one of the major differences between switched singular systems and switched normal systems, which make the problem for switched singular systems more difficult. There are some results on inconsistent initial condition at switching instants reported in . Some literature consider the state instantaneous jumps as known structure .…”

Section: Introductionmentioning

confidence: 99%

“…Some literature consider the state instantaneous jumps as known structure . Some literature express the state instantaneous jumps based on the switched singular system matrices , and the work of authors in are further results of . However, to the best of our knowledge, for the second method , there are limited results designing controller, weakening the state instantaneous jumps or reducing the average dwell time caused by state instantaneous jumps.…”

Section: Introductionmentioning

confidence: 99%

RobustH_∞control for switched singular linear systems with uncertainties in the derivative matrices: an improved average dwell time approach

Zhai

et al. 2015

Optim. Control Appl. Meth.

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Summary This paper addresses the robust H∞ control problem for continuous‐time switched singular systems with uncertainties in the state, input, and derivative matrices. A two‐phase method is proposed in this paper to optimize H∞ performance and to minimize the upper bound of the average dwell time. First, sufficient conditions for finding a state feedback controller guaranteeing the minimum H∞ disturbance attenuation are proposed. Besides, the average dwell time is obtained by solving linear matrices inequalities introduced in this paper. Second, to minimize the upper bound of the average dwell time, an improve average dwell time approach is put forward by introducing a new technique. And based on the result in the first phase, a new feedback controller, which optimizes H∞ performance and minimizes the upper bound of the average dwell time is obtained by using the improved average dwell time approach. The point is that when the upper bound of the average dwell time is decreasing, H∞ disturbance attenuation will increase and vice versa. Therefore, a trade‐off should be built between H∞ disturbance attenuation and average dwell time in practice. Finally, several numerical examples are presented to illustrate the effectiveness of the methods proposed. Copyright © 2015 John Wiley & Sons, Ltd.

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Continuous fixed-time convergent controller for permanent-magnet synchronous motor with unbounded perturbations

Rodriguez‐Ramirez

Ramos-Lopez

2020

Journal of the Franklin Institute

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Finite-time Stability Analysis of Switched Linear Singular Systems

Cited by 4 publications

References 33 publications

Observability of Singular Linear Switched Systems in Discrete Time: Single Switch Case

Observability of Singular Linear Switched Systems in Discrete Time: Single Switch Case

RobustH_∞control for switched singular linear systems with uncertainties in the derivative matrices: an improved average dwell time approach

Continuous fixed-time convergent controller for permanent-magnet synchronous motor with unbounded perturbations

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Finite-time Stability Analysis of Switched Linear Singular Systems

Cited by 4 publications

References 33 publications

Observability of Singular Linear Switched Systems in Discrete Time: Single Switch Case

Observability of Singular Linear Switched Systems in Discrete Time: Single Switch Case

RobustH∞control for switched singular linear systems with uncertainties in the derivative matrices: an improved average dwell time approach

Continuous fixed-time convergent controller for permanent-magnet synchronous motor with unbounded perturbations

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RobustH_∞control for switched singular linear systems with uncertainties in the derivative matrices: an improved average dwell time approach