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

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

doi:10.1109/tac.2020.2968580

Cited by 35 publications

(23 citation statements)

References 54 publications

(142 reference statements)

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“…The ISS and iISS properties are called "strong" because the decaying term given by the function β forces additional decay whenever a jump occurs. The corresponding weak properties are obtained by replacing the second argument of β by t − t 0 (see Mancilla-Aguilar and Haimovich, 2019). Strong ISS (and iISS) is in agreement with the ISS property for hybrid systems as in Liberzon et al (2014).…”

Section: Stability Definitionssupporting

confidence: 54%

“…Since the appearance of Hespanha et al (2008), many works have addressed the stability of impulsive systems with inputs from ISS-related standpoints, giving sufficient conditions for the ISS and/or iISS in terms of Lyapunov functions (Chen and Zheng, 2009;Liu et al, 2011;Dashkovskiy et al, 2012;Dashkovskiy and Mironchenko, 2013b;Liu et al, 2014;Li et al, 2017;Dashkovskiy and Feketa, 2017;Li et al, 2018;Peng et al, 2018;Peng, 2018;Ning et al, 2018;Li and Li, 2019;Mancilla-Aguilar and Haimovich, 2019). In addition, some results for hybrid systems may also be applicable to impulsive systems (Liberzon et al, 2014;Mironchenko et al, 2018;Liu et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A characterization of strong iISS for time-varying impulsive systems

Haimovich¹,

Mancilla-Aguilar

Cardone

2019

2019 XVIII Workshop on Information Processing and Control (RPIC)

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For time-invariant (nonimpulsive) systems, it is already well-known that the input-to-state stability (ISS) property is strictly stronger than integral input-to-state stability (iISS). Very recently, we have shown that under suitable uniform boundedness and continuity assumptions on the function defining system dynamics, ISS implies iISS also for time-varying systems. In this paper, we show that this implication remains true for impulsive systems, provided that asymptotic stability is understood in a sense stronger than usual for impulsive systems. extension to classes of systems for which Lyapunov characterizations do not exist, such as switched systems under restricted switching or impulsive systems. Very recently, Haimovich and Mancilla-Aguilar (2019) proved that ISS implies iISS for families of time-varying and switched nonlinear systems without resorting to any Lyapunov converse theorem, and, in this way, opening the door to proving the implication for other types of systems.

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Section: Stability Definitionssupporting

confidence: 54%

Section: Introductionmentioning

confidence: 99%

A characterization of strong iISS for time-varying impulsive systems

Haimovich¹,

Mancilla-Aguilar

Cardone

2019

2019 XVIII Workshop on Information Processing and Control (RPIC)

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“…This note considers stability properties where convergence is ensured not only as time elapses but also as the number of occurring impulses increases (see [23], [21] for background). For an impulsetime sequence σ ∈ Γ, let n σ (s,t] denote the number of impulse times lying in the interval (s, t], that is…”

Section: Stabilitymentioning

confidence: 99%

“…Requiring convergence not only as continuous time advances but also as the number of occurring impulses increases leads to a stronger notion of stability that allows to recover, for impulsive systems, many of the robustness properties exhibited by nonimpulsive systems [21], [22]. Moreover, this stronger stability notion becomes equivalent to the weak and most usual one whenever the number of occurring impulses can be bounded in correspondence with the length of the time interval over which they occur [23,Proposition 2.3]; this happens, e.g., when the continuous evolution (i.e. between impulses) has a minimum, average or fixed dwell time.…”

Section: Introductionmentioning

confidence: 99%

(Integral-)ISS of switched and time-varying impulsive systems based on global state weak linearization

Mancilla-Aguilar¹,

Haimovich²

2021

Preprint

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It is shown that impulsive systems of nonlinear, time-varying and/or switched form that allow a stable global state weak linearization are jointly input-to-state stable (ISS) under small inputs and integral ISS (iISS). The system is said to allow a global state weak linearization if its flow and jump equations can be written as a (time-varying, switched) linear part plus a (nonlinear) pertubation satisfying a bound of affine form on the state. This bound reduces to a linear form under zero input but does not force the system to be linear under zero input. The given results generalize and extend previously existing ones in many directions: (a) no (dwell-time or other) constraints are placed on the impulse-time sequence, (b) the system need not be linear under zero input, (c) existence of a (common) Lyapunov function is not required, (d) the perturbation bound need not be linear on the input.

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“…In general, the impulse control method is based on the theory of impulsive differential equations. Researchers studied the asymptotic stability of the impulse control system by using the Lyapunov method [16][17][18] and the comparison theorem [19]. Among the published impulse control methods, some control strategies require to adjust all state variables [20][21][22], others achieve the goal by manipulating only one state variable [23][24], but only [25] dealt with the perturbation of a parameter, as required in our work.…”

Section: Introductionmentioning

confidence: 99%

Bi-directional impulse chaos control in crystal growth

Zhou

Ren

Grebogi

2021

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Mono-silicon crystals, free of defects, are essential for the Integrated Circuit industry. Chaotic swing in the flexible shaft rotating-lifting (FSRL) system of the mono-silicon crystal puller causes harm to the quality of the crystal and must be suppressed in the crystal growth procedure. From the control system viewpoint, the constraints of the FSRL system can be summarized as not having measurable state variables for state feedback control, and only one parameter is available to be manipulated, namely, the rotation speed. From the application side, an additional constraint is that the control should affect the crystallization physical growth process as little as possible. These constraints make the chaos suppression in the FSRL system to be a challenging task. In this work, the analytical periodic solution of the swing in the FSRL system is derived using perturbation analysis. A bi-directional impulse control method is then proposed for suppressing chaos. This control method does not alter the average rotation speed. It is thus optimum regarding the crystallization process as compared with the single direction impulse control. The effectiveness and robustness of the proposed chaos control method to parameters uncertainties are validated by the simulations.

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

Cited by 35 publications

References 54 publications

A characterization of strong iISS for time-varying impulsive systems

A characterization of strong iISS for time-varying impulsive systems

(Integral-)ISS of switched and time-varying impulsive systems based on global state weak linearization

Bi-directional impulse chaos control in crystal growth

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