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Lyapunov-Based Stability and Construction of Lyapunov Functions for Boolean Networks
SIAM Journal on Control and Optimization, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Li Haitao
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Semidefinite lyapunov functions stability and stabilization
Mathematics of Control, Signals, and Systems, 1996The paper gives some weakening of the basic Lyapunov theorems by obtaining stability and asymptotic stability for nonnegatively definite Lyapunov functions. These results allow simpler proofs for some previously known results and some extension of the stabilization results for systems that are affine in the control.
Iggidr, Abderrahman +2 more
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Connecting nonlinear incremental Lyapunov stability with the linearizations Lyapunov stability
Proceedings of the 44th IEEE Conference on Decision and Control, 2006In this paper, we reveal new connections between the incremental Lyapunov properties of a nonlinear system and the Lyapunov properties of its linearizations. We focus on (incremental) asymptotic and exponential stability. In contrast with other works on the incremental Lyapunov properties of nonlinear systems, our approach is based on extended spaces ...
Fromion, Vincent, Scorletti, Gérard
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Lyapunov Theory for Zeno Stability
IEEE Transactions on Automatic Control, 2013Zeno behavior is a dynamic phenomenon unique to hybrid systems in which an infinite number of discrete transitions occurs in a finite amount of time. This behavior commonly arises in mechanical systems undergoing impacts and optimal control problems, but its characterization for general hybrid systems is not completely understood.
Andrew G. Lamperski, Aaron D. Ames
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A Lyapunov approach in incremental stability
IEEE Conference on Decision and Control and European Control Conference, 2011The notion of incremental stability was proposed by several researchers as a strong property of dynamical and control systems. Incremental stability describes the convergence of trajectories with respect to themselves, rather than with respect to an equilibrium point or a particular trajectory.
Majid Zamani 0001, Rupak Majumdar
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Does Neutral Stability Imply Lyapunov Stability?
Games and Economic Behavior, 1995zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bomze, Immanuel M., Weibull, Jörgen W.
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A Lyapunov approach to incremental stability
Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), 2002This paper deals with several notions of incremental stability. In other words, we focus on the stability of trajectories with respect to one another, rather than with respect some attractor or equilibrium point. The aim is to present a framework for understanding such questions fully compatible with the well-known input-to-state stability approach.
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