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Computation of Piecewise Quadratic Lyapunov Functions for Hybrid Systems
 IEEE Transactions on Automatic Control
, 1998
"... . This paper presents a computational approach to stability analysis of nonlinear and hybrid systems. The search for a piecewise quadratic Lyapunov function is formulated as a convex optimization problem in terms of linear matrix inequalities. The relation to frequency domain methods such as the cir ..."
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Cited by 259 (4 self)
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. This paper presents a computational approach to stability analysis of nonlinear and hybrid systems. The search for a piecewise quadratic Lyapunov function is formulated as a convex optimization problem in terms of linear matrix inequalities. The relation to frequency domain methods
Using Extended Lyapunov Function and
, 2005
"... Large disturbance voltage stability assessment using extended Lyapunov function and considering voltage dependent active loads ..."
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Large disturbance voltage stability assessment using extended Lyapunov function and considering voltage dependent active loads
Feedback stabilization and Lyapunov functions
"... Given a locally defined, nondifferentiable but Lipschitz Lyapunov function, we construct a (discontinuous) feedback law which stabilizes the underlying system to any given tolerance. A further result shows that suitable Lyapunov functions of this type exist under mild assumptions. We also establish ..."
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Cited by 25 (7 self)
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Given a locally defined, nondifferentiable but Lipschitz Lyapunov function, we construct a (discontinuous) feedback law which stabilizes the underlying system to any given tolerance. A further result shows that suitable Lyapunov functions of this type exist under mild assumptions. We also
Lower Semicontinuous Lyapunov Functions and
"... We show that lower semicontinuous Lyapunov functions can be used to determine both stable and attractive sets of differential equations with a short proof similar to that of the original Lyapunov indirect method. Several examples illustrate the flexibility of using such lower semicontinuous Lyapu ..."
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We show that lower semicontinuous Lyapunov functions can be used to determine both stable and attractive sets of differential equations with a short proof similar to that of the original Lyapunov indirect method. Several examples illustrate the flexibility of using such lower semicontinuous
Feedback stabilization and Lyapunov functions
 SIAM J. CONTROL OPTIM
"... Given a locally defined, nondifferentiable but Lipschitz Lyapunov function, we employ it in order to construct a (discontinuous) feedback law which stabilizes the underlying system to any given tolerance. A converse result shows that suitable Lyapunov functions of this type exist under mild assump ..."
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Cited by 20 (2 self)
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Given a locally defined, nondifferentiable but Lipschitz Lyapunov function, we employ it in order to construct a (discontinuous) feedback law which stabilizes the underlying system to any given tolerance. A converse result shows that suitable Lyapunov functions of this type exist under mild
Lyapunov functionals and L
, 2002
"... We devise Lyapunov functionals and prove uniform L stability for onedimensional semilinear hyperbolic systems with quadratic nonlinear source terms. These systems encompass a class of discrete velocity models for the Boltzmann equation. The Lyapunov functional is equivalent to the L distan ..."
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We devise Lyapunov functionals and prove uniform L stability for onedimensional semilinear hyperbolic systems with quadratic nonlinear source terms. These systems encompass a class of discrete velocity models for the Boltzmann equation. The Lyapunov functional is equivalent to the L
AN ALGORITHM FOR CONSTRUCTING LYAPUNOV FUNCTIONS
, 2007
"... In this monograph we develop an algorithm for constructing Lyapunov functions for arbitrary switched dynamical systems ˙x = fσ(t, x), possessing a uniformly asymptotically stable equilibrium. Let ˙x = fp(t, x), p ∈ P, be the collection of the ODEs, to which the switched system corresponds. The numbe ..."
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Cited by 7 (6 self)
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In this monograph we develop an algorithm for constructing Lyapunov functions for arbitrary switched dynamical systems ˙x = fσ(t, x), possessing a uniformly asymptotically stable equilibrium. Let ˙x = fp(t, x), p ∈ P, be the collection of the ODEs, to which the switched system corresponds
Nonsmooth ControlLyapunov Functions
 Proc. IEEE Conf. Decision and Control
, 1995
"... It is shown that the existence of a continuous controlLyapunov function (CLF) is necessary and sufficient for null asymptotic controllability of nonlinear finitedimensional control systems. The CLF condition is expressed in terms of a concept of generalized derivative that has been studied in setva ..."
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Cited by 42 (7 self)
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It is shown that the existence of a continuous controlLyapunov function (CLF) is necessary and sufficient for null asymptotic controllability of nonlinear finitedimensional control systems. The CLF condition is expressed in terms of a concept of generalized derivative that has been studied in set
nonlinearitydependent Lyapunov function
, 2008
"... A class of switched nonquadratic Lyapunov functions is considered in this paper. The function is associated with discretetime switched systems subject to modedependent cone bounded nonlinearities and saturation actuator. These Lyapunov functions depend on the switched nonlinearities and on the ac ..."
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A class of switched nonquadratic Lyapunov functions is considered in this paper. The function is associated with discretetime switched systems subject to modedependent cone bounded nonlinearities and saturation actuator. These Lyapunov functions depend on the switched nonlinearities
Results 1  10
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3,658