Results 11 to 20 of about 625,732 (254)
Computation and Verification of Lyapunov Functions [PDF]
SIAM Journal on Applied Dynamical Systems, 2015 Lyapunov functions are an important tool to determine the basin of attraction of equilibria in Dynamical Systems through their sublevel sets. Recently, several numerical construction methods for Lyapunov functions have been proposed, among them the RBF (Radial Basis Function) and CPA (Continuous Piecewise Affine) methods. While the first method lacks a
Peter Giesl, Sigurdur F. Hafstein
openaire +4 more sources
Time-dependent mode structure for Lyapunov vectors as a collective movement in quasi-one-dimensional systems [PDF]
Phys. Rev. E71, 016218 (2005), 2004 Time dependent mode structure for the Lyapunov vectors associated with the stepwise structure of the Lyapunov spectra and its relation to the momentum auto-correlation function are discussed in quasi-one-dimensional many-hard-disk systems. We demonstrate mode structures (Lyapunov modes) for all components of the Lyapunov vectors, which include the ...
Gary P. Morriss +10 more
arxiv +3 more sources
Lyapunov Modes and Time-Correlation Functions for Two-Dimensional Systems [PDF]
, 2005 The relation between the Lyapunov modes (delocalized Lyapunov vectors) and the momentum autocorrelation function is discussed in two-dimensional hard-disk systems. We show numerical evidence that the smallest time-oscillating period of the Lyapunov modes is twice as long as the time-oscillating period of momentum autocorrelation function for both ...
Morriss, Gary P., Taniguchi, Tooru
arxiv +6 more sources
Existence of complete Lyapunov functions for semiflows on separable metric spaces [PDF]
arXiv, 2011 The aim of this short note is to show how to construct a complete Lyapunov function of a semiflow by using a complete Lyapunov function of its time-one map. As a byproduct we assure the existence of complete Lyapunov functions for semiflows on separable metric spaces.
Patrão, Mauro
arxiv +3 more sources
Further Results on Lyapunov Functions for Slowly Time-Varying Systems [PDF]
Mathematics of Control Signals and Systems, Volume 19, Number 1,
pp. 1-21, February 2007, 2006 We provide general methods for explicitly constructing strict Lyapunov functions for fully nonlinear slowly time-varying systems. Our results apply to cases where the given dynamics and corresponding frozen dynamics are not necessarily exponentially stable. This complements our previous Lyapunov function constructions for rapidly time-varying dynamics.
Malisoff, Michael, Mazenc, Frederic
arxiv +5 more sources
Lyapunov Functions in Piecewise Linear Systems: From Fixed Point to Limit Cycle [PDF]
arXiv, 2013 This paper provides a first example of constructing Lyapunov functions in a class of piecewise linear systems with limit cycles. The method of construction helps analyze and control complex oscillating systems through novel geometric means. Special attention is stressed upon a problem not formerly solved: to impose consistent boundary conditions on the
Ao, Ping +4 more
arxiv +3 more sources
Lower Bounds on Complexity of Lyapunov Functions for Switched Linear Systems [PDF]
, 2015 We show that for any positive integer $d$, there are families of switched linear systems---in fixed dimension and defined by two matrices only---that are stable under arbitrary switching but do not admit (i) a polynomial Lyapunov function of degree $\leq
Ahmadi, Amir Ali, Jungers, Raphael
core +2 more sources
Construction of time-varying ISS-Lyapunov Functions for Impulsive Systems [PDF]
, 2022 Time-varying ISS-Lyapunov functions for impulsive systems provide a necessary and sufficient condition for ISS. This property makes them a more powerful tool for stability analysis than classical candidate ISS-Lyapunov functions providing only a sufficient ISS condition.
arxiv +1 more source
Stabilization of Nonlinear Control-Affine Systems With Multiple State Constraints
IEEE Access, 2020 This paper considers the synthesis of stabilizing controllers for nonlinear control-affine systems under multiple state constraints. A new control Lyapunov-barrier function approach is introduced for solving the considered problem.
Jia-Yao Jhang +2 more
doaj +1 more source
Gap Functions and Lyapunov Functions
Journal of Global Optimization, 2004 Equilibrium problems play a central role in the study of complex and competitive systems. Many variational formulations of these problems have been presented in these years. So, variational inequalities are very useful tools for the study of equilibrium solutions and their stability.
PAPPALARDO, MASSIMO +1 more
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