Stabilization of continuous-time singularly perturbed switched systems

Malloci, Ivan; Daafouz, Jamal; Iung, Claude

doi:10.1109/cdc.2009.5399876

Cited by 33 publications

(38 citation statements)

References 17 publications

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“…Multiple timescale switched systems 40 are of practical interest in many applications. The stability of continuous-time switched linear systems in the singular perturbation form has been investigated in [21]. It is shown that the stability of slow and fast switched subsystems is not sufficient for the stability of the corresponding two-timescale switched systems.…”

Section: Introductionmentioning

confidence: 99%

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Exponential stabilization of singularly perturbed switched systems subject to actuator saturation

Lian¹,

Wang²

2015

Information Sciences

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Section: Introductionmentioning

confidence: 99%

“…Up to now, few research works have focused on singularly perturbed systems with actuation saturation [21,30]. The stabilization of singularly perturbed systems subject to actuator saturation has been studied in [21].…”

Section: Introductionmentioning

confidence: 99%

Exponential stabilization of singularly perturbed switched systems subject to actuator saturation

Lian¹,

Wang²

2015

Information Sciences

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“…However, there are also studies on nonlinear agents such as oscillators dynamics (Steur et al 2009, nonholonomic robots (Bullo et al 2009) or general nonlinear systems (Buşoniu & Morȃrescu 2014). On the other hand, one can find many applications ranging from biological systems such as gene expression systems (L.Chen & Aihara 2002), neurons behavior (Hodgkin & Huxley 1952) to engineering problems (Malloci et al 2009) that involve processes evolving on different time-scales. General stability and stabilization of such linear and non-linear systems, called singularly perturbed, can be found in (Kokotović et al 1999, Khalil 2001.…”

Section: Introductionmentioning

confidence: 99%

Control design with guaranteed cost for synchronization in networks of linear singularly perturbed systems

2018

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To cite this version:Jihene Ben Rejeb, Irinel-Constantin Morarescu, Jamal Daafouz. Control design with guaranteed cost for synchronization in networks of linear singularly perturbed systems. Automatica, Elsevier, 2018, 91, pp.89-97. 10.1016/j.automatica.2018 Control design with guaranteed cost for synchronization in networks of linear singularly perturbed systems AbstractThis work presents the design of a decentralized control strategy that allows singularly perturbed multi-agent systems to achieve synchronization with global performance guarantees. The study is mainly motivated by the presence of two features that characterize many physical systems. The first is the complexity in terms of interconnected subsystems and the second is that each subsystem involves processes evolving on different time-scales. In the context of interconnected systems, the decentralized control is interesting since it considerably reduces the communication load (and the associated energy) which can be very important when dealing with centralized policies. Therefore, the main difficulty that we have to overcome is that we have to avoid the use of centralized information related to the interconnection network structure. This problem is solved by rewriting the synchronization problem in terms of stabilization of a singularly perturbed uncertain linear system. The singularly perturbed dynamics of subsystems generates theoretical challenges related to the stabilizing controller design but also numerical issues related to the computation of the controller gains. We show that these problems can be solved by decoupling the slow and fast dynamics. Our theoretical developments are illustrated by some numerical examples.

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“…On the other hand, there are many applications ranging from biological systems such as gene expression systems [6], neurons behavior [7] to engineering problems [8] that involve processes evolving on different time-scales. One can find many contributions with general stability and stabilization results for such linear and nonlinear multiple time scale systems (see [9] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Guaranteed cost control design for synchronization in networks of linear singularly perturbed systems

Rejeb

Morărescu

Daafouz

2017

2017 IEEE 56th Annual Conference on Decision and Control (CDC)

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Abstract-This work presents the design of a decentralized control strategy that allows singularly perturbed multi-agent systems to achieve synchronization with global performance guarantees. The study is mainly motivated by the presence of two features that characterize many physical systems. The first is the complexity in terms of interconnected subsystems and the second is that each subsystem involves processes evolving on different time-scales. The main difficulty that we have to overcome is that we have to avoid the use of centralized information related to the interconnection network structure. This problem is solved by rewriting the synchronization problem in terms of stabilization of a singularly perturbed uncertain linear system. The singularly perturbed dynamics of subsystems generates theoretical challenges related to the stabilizing controller design but also numerical issues related to the computation of the controller gains. We show that these problems can be solved by decoupling the slow and fast dynamics. Our theoretical developments are illustrated by some numerical examples.

show abstract

Stabilization of continuous-time singularly perturbed switched systems

Cited by 33 publications

References 17 publications

Exponential stabilization of singularly perturbed switched systems subject to actuator saturation

Exponential stabilization of singularly perturbed switched systems subject to actuator saturation

Control design with guaranteed cost for synchronization in networks of linear singularly perturbed systems

Guaranteed cost control design for synchronization in networks of linear singularly perturbed systems

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