Transverse contraction criteria for stability of nonlinear hybrid limit cycles

Tang, J.; Manchester, Ian R.

doi:10.1109/cdc.2014.7039355

Cited by 15 publications

(14 citation statements)

References 25 publications

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“…An extension to piecewise smooth continuous (PWSC) systems was outlined in (Lohmiller and Slotine, 2000) and formalized in . Contracting hybrid systems were analysed in (Lohmiller and Slotine, 2000) while the stability analysis of hybrid limit cycles using contraction was presented in (Tang and Manchester, 2014). An extension of contraction theory, related to the concept of weak contraction (Sontag et al, 2015), to characterize incremental stability of sliding mode solutions of planar Filippov systems was first presented in (di Bernardo and Liuzza, 2013) and later extended to n-dimensional Filippov systems in (di Bernardo and Fiore, 2014).…”

Section: Introductionmentioning

confidence: 99%

Contraction analysis of switched systems via regularization

2016

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We study incremental stability and convergence of switched (bimodal) Filippov systems via contraction analysis. In particular, by using results on regularization of switched dynamical systems, we derive sufficient conditions for convergence of any two trajectories of the Filippov system between each other within some region of interest. We then apply these conditions to the study of different classes of Filippov systems including piecewise smooth (PWS) systems, piecewise affine (PWA) systems and relay feedback systems. We show that contrary to previous approaches, our conditions allow the system to be studied in metrics other than the Euclidean norm. The theoretical results are illustrated by numerical simulations on a set of representative examples that confirm their effectiveness and ease of application

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Section: Introductionmentioning

confidence: 99%

Contraction analysis of switched systems via regularization

2016

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“…In this way, one can analyze the stability analytically and characterize the stability region. For more information, the reader can refer to [13][14][15].…”

Section: Transverse Dynamicsmentioning

confidence: 99%

A Data Driven Vector Field Oscillator with Arbitrary Limit Cycle Shape

Pasandi¹,

Dinale²,

Keshmiri³

et al. 2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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Cyclic motions in vertebrates, including heart beating, breathing and walking, are derived by a network of biological oscillators having fascinating features such as entrainment, environment adaptation and robustness. These features encouraged engineers to use oscillators for generating cyclic motions. To this end, it is crucial to have oscillators capable of characterizing any periodic signal via a stable limit cycle. In this paper, we propose a 2-dimensional oscillator whose limit cycle can be matched to any periodic signal depicting a non-self-intersecting curve in the state space. In particular, the proposed oscillator is designed as an autonomous vector field directed toward the desired limit cycle. To this purpose, the desired reference signal is parameterized with respect to a state-dependent phase variable, then the oscillator's states track the parameterized signal. We also present a state transformation technique to bound the oscillator's output and its first time derivative. The soundness of the proposed oscillator has been verified by carrying out a few simulations. * a

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“…In [9], a method for efficiently computing contraction metrics was introduced which employs methods based on sums-of-squares programs proposed in [10] for the efficient computational verification of polynomial positivity. This computational approach was extended in [11] and [12] to compute contraction metrics to verify local ROCs of systems with limit cycles. We apply this approach to a commonly used model for kite controller design, and extend it by both maximizing for larger estimates of ROCs as well as by considering parametric affine uncertainty in the system dynamics.…”

Section: Introductionmentioning

confidence: 99%