Switch observability for switched linear systems

This paper addresses the observability analysis and the observer design of the continuous state for a particular class of linear switched systems. Using some dynamical properties of considered systems, we give a simple necessary and sufficient condition of the observability for a predetermined switching sequence. The obtained observability condition leads us to design a new real time state observer. This latter is based on the exact accumulation of the information provided from the switching sequence of modes, and it convergences once the observability condition is verified. Some examples with simulation show the efficiency of the obtain observability condition and the proposed state observer.

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“…is the classical observability matrix [14][15][16][17][18][19] of mode j σ , and…”

Section: Observability Analysismentioning

confidence: 99%

Observability and Observer Design of a Class of Switched Linear Systems

Gherraf¹,

Haddadi²,

Benalia³

2021

EEA

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“…As for [8], an extended system containing both the plant and the observer is directly analyzed. In the particular setting of switched systems, the problem is handled by estimating the switching signal, whose observability has been studied in [9,10]. Some observer designs exist based on the detection and identification of switches ( [11,12,13,14]).…”

Section: Contextmentioning

confidence: 99%

On Notions of Detectability and Observers for Hybrid Systems

Bernard

Sanfelice

2020

2020 59th IEEE Conference on Decision and Control (CDC)

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An asymptotic observer is a dynamical system taking as input the plant's output and producing asymptotically an estimate of the plant's state. It is commonly known that for an observer to exist, the plant must be asymptotically detectable, namely the trajectories giving the same output must asymptotically converge to one another. But unlike continuous-time and discrete-time systems, those notions are not straightforward to define for a hybrid plant, since solutions do not share the same hybrid time domain. In this paper, we propose to define observers and detectability for hybrid systems together, in a way that ensures detectability remains necessary for the existence of an observer and such that standard definitions are recovered for continuous-time and discrete-time systems. We rely on the recent definition of hybrid systems with hybrid inputs and use jump reparametrizations to define convergence and equality of outputs.

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“…Although there are a variety of research studies in the area of switched systems (Baglietto et al, 2013; Baleghi and Shafiei, 2019; Cao et al, 2015; Goodwin et al, 2010; Kermani et al, 2014; Morse, 1997; Varaiya, 1993; Wang et al, 2017; Zhai et al, 2017; Zhang et al, 2017), the main theoretical contributions are handily summed up in two points. The first point is the considerable efforts devoted to the detection and recognition of the active mode (Blanchini et al, 2009; Küsters and Trenn, 2018; Lee and Dullerud, 2006; Xie and Wu, 2009). The second one is the primary attention addressed to the problems of regulation and stabilization around zero (Aoun et al, 2017; Baglietto et al, 2013; Baleghi and Shafiei, 2019; Kermani et al, 2014; Liu et al, 2017; Sun and Ge, 2001; Xie and Wang, 2005; Yin et al, 2017; Wang et al, 2017).…”

Section: Introductionmentioning

confidence: 99%

Dynamic multi-objective matrix control for a class of switched systems

Thamallah

Sakly

M’Śahli

2021

Transactions of the Institute of Measurement and Control

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This article focuses on the tracking and stabilizing issues of a class of discrete switched systems. These systems are characterized by unknown switching sequences, a non-minimum phase, and time-varying or dead modes. In particular, for those governed by an indeterminate switching signal, it is very complicated to synthesize a control law able to systematically approach general reference-tracking difficulties. Taking into account the difficulty to express the dynamic of this class of systems, the present paper presents a new Dynamic matrix control method based on the multi-objective optimization and the truncated impulse response model. The formulation of the optimization problem aims to approach the general step-tracking issues under persistent and indeterminate mode changes and to overcome the stability problem along with retaining as many desirable features of the standard dynamic matrix control (DMC) method as possible. In addition, the formulated optimization problem integrates estimator variables able to manipulate the optimization procedure in favor of the active mode with an appropriate adjustment. It also provides a progressive and smooth multi-objective control law even in the presence of problems whether in subsystems or switching sequences. Finally, simulation examples and comparison tests are conducted to illustrate the potentiality and effectiveness of the developed method.

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Switch observability for switched linear systems

Cited by 42 publications

References 9 publications

Observability and Observer Design of a Class of Switched Linear Systems

Observability and Observer Design of a Class of Switched Linear Systems

On Notions of Detectability and Observers for Hybrid Systems

Dynamic multi-objective matrix control for a class of switched systems

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