Nonrobustness of asymptotic stability of impulsive systems with inputs

Haimovich, Hernan; Mancilla-Aguilar, J.L.

doi:10.1016/j.automatica.2020.109238

Cited by 7 publications

(4 citation statements)

References 27 publications

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“…In addition, for such a stronger stability property it is possible to show that ISS implies integral ISS [30]. Another reason for considering this strong stability property is that it is robust [31], whereas the weak counterpart is not [32].…”

Section: Introductionmentioning

confidence: 99%

Uniform Input-To-State Stability for Switched and Time-Varying Impulsive Systems

Mancilla-Aguilar

Haimovich

2020

IEEE Trans. Automat. Contr.

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We provide a Lyapunov-function-based method for establishing different types of uniform input-to-state stability (ISS) for time-varying impulsive systems. The method generalizes to impulsive systems with inputs the well-established philosophy of assessing the stability of a system by reducing the problem to that of the stability of a scalar system given by the evolution of the Lyapunov function on the system trajectories. This reduction is performed in such a way so that the resulting scalar system has no inputs. Novel sufficient conditions for ISS are provided, which generalize existing results for time-invariant and timevarying, switched and nonswitched, impulsive and nonimpulsive systems in several directions.

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Section: Introductionmentioning

confidence: 99%

Uniform Input-To-State Stability for Switched and Time-Varying Impulsive Systems

Mancilla-Aguilar

Haimovich

2020

IEEE Trans. Automat. Contr.

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“…The weak ISS property is the one considered in most of the literature on impulsive systems with inputs, whereas strong ISS is in agreement with the ISS property for hybrid systems as in Liberzon et al (2014). The weak stability properties are, however, not robust in the context of time-varying systems (see Haimovich and Mancilla-Aguilar, 2019a).…”

Section: Input-to-state Stability (Iss)mentioning

confidence: 62%

“…The majority of results on stability of impulsive systems consider a bound on the state that decays as time elapses but is insensitive to the occurrence of jumps. In a time-varying setting, this stability notion is not robust and too weak to be meaningful, as shown in Haimovich and Mancilla-Aguilar (2019a). By contrast, a stronger stability concept where the bound on the state also decays when jumps occur, as usually considered for hybrid systems (Cai and Teel, 2009), indeed is robust and more meaningful for impulsive systems in a time-varying setting (Haimovich and Mancilla-Aguilar, 2019b).…”

Section: Introductionmentioning

confidence: 99%

Uniform stability of nonlinear time-varying impulsive systems with eventually uniformly bounded impulse frequency

Mancilla-Aguilar¹,

Haimovich²,

Feketa³

2019

Preprint

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We provide novel sufficient conditions for stability of nonlinear and time-varying impulsive systems. These conditions generalize, extend, and strengthen many existing results. Different types of input-to-state stability (ISS), as well as zero-input global uniform asymptotic stability (0-GUAS), are covered by employing a twomeasure framework and considering stability of both weak (decay depends only on elapsed time) and strong (decay depends on elapsed time and the number of impulses) flavors. By contrast to many existing results, the stability state bounds imposed are uniform with respect to initial time and also with respect to classes of impulse-time sequences where the impulse frequency is eventually uniformly bounded. We show that the considered classes of impulse-time sequences are substantially broader than other previously considered classes, such as those having fixed or (reverse) average dwell times, or impulse frequency achieving uniform convergence to a limit (superior or inferior). Moreover, our sufficient conditions are not more restrictive than existing ones when particularized to some of the cases covered in the literature, and hence in these cases our results allow to strengthen the existing conclusions.

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“…Switched systems and impulsive systems are two general classes of hybrid systems. Switched systems involve a finite number of constituent modes and a switching signal orchestrating the switching between them [3], while impulsive systems depict real world processes that generate instantaneous state resets at discrete times [4]. Impulsive switched system, as a more comprehensive dynamical system, involves impulses and switching in a single framework [5].…”

Section: Dear Editormentioning

confidence: 99%

Lyapunov Conditions for Finite-Time Input-to-State Stability of Impulsive Switched Systems

Zhang,

Cao,

2024

IEEE/CAA J. Autom. Sinica

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Nonrobustness of asymptotic stability of impulsive systems with inputs

Cited by 7 publications

References 27 publications

Uniform Input-To-State Stability for Switched and Time-Varying Impulsive Systems

Uniform Input-To-State Stability for Switched and Time-Varying Impulsive Systems

Uniform stability of nonlinear time-varying impulsive systems with eventually uniformly bounded impulse frequency

Lyapunov Conditions for Finite-Time Input-to-State Stability of Impulsive Switched Systems

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