Results 1  10
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102,145
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
Flexible control Lyapunov functions
 American Control Conference
, 2009
"... Abstract — A central tool in systems theory for synthesizing control laws that achieve stability are control Lyapunov functions (CLFs). Classically, a CLF enforces that the resulting closedloop state trajectory is contained within a cone with a fixed, predefined shape, and which is centered at and ..."
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Cited by 7 (7 self)
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Abstract — A central tool in systems theory for synthesizing control laws that achieve stability are control Lyapunov functions (CLFs). Classically, a CLF enforces that the resulting closedloop state trajectory is contained within a cone with a fixed, predefined shape, and which is centered
Smooth patchy control Lyapunov functions
, 2006
"... A smooth patchy control Lyapunov function for a nonlinear system consists of an ordered family of smooth local control Lyapunov functions, whose open domains form a locally finite cover of the state space of the system, and which satisfy a decrease condition when the domains overlap. We prove that ..."
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Cited by 7 (2 self)
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A smooth patchy control Lyapunov function for a nonlinear system consists of an ordered family of smooth local control Lyapunov functions, whose open domains form a locally finite cover of the state space of the system, and which satisfy a decrease condition when the domains overlap. We prove
General Classes Of ControlLyapunov Functions
, 1995
"... The main result of this paper establishes the equivalence between null asymptotic controllability of nonlinear finitedimensional control systems and the existence of continuous controlLyapunov functions (clf's) defined by means of generalized derivatives. In this manner, one obtains a compl ..."
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Cited by 3 (0 self)
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The main result of this paper establishes the equivalence between null asymptotic controllability of nonlinear finitedimensional control systems and the existence of continuous controlLyapunov functions (clf's) defined by means of generalized derivatives. In this manner, one obtains a
LOWER BOUNDED CONTROLLYAPUNOV FUNCTIONS ∗
"... Abstract. The well known Brockett condition a topological obstruction to the existence of smooth stabilizing feedback laws has engendered a large body of work on discontinuous feedback stabilization. The purpose of this paper is to introduce a class of controlLyapunov function from which it is po ..."
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Cited by 1 (0 self)
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Abstract. The well known Brockett condition a topological obstruction to the existence of smooth stabilizing feedback laws has engendered a large body of work on discontinuous feedback stabilization. The purpose of this paper is to introduce a class of controlLyapunov function from which
Weak converse Lyapunov theorems and control Lyapunov functions
 SIAM J. Control Optim
, 2004
"... Abstract. Given a weakly uniformly globally asymptotically stable closed (not necessarilycompact) set A for a differential inclusion that is defined on R n, is locallyLipschitz on R n \A, and satisfies other basic conditions, we construct a weak Lyapunov function that is locally Lipschitz on R n. Us ..."
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Cited by 10 (2 self)
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. Using this result, we show that uniform global asymptotic controllabilityto a closed (not necessarilycompact) set for a locallyLipschitz nonlinear control system implies the existence of a locallyLipschitz controlLyapunov function, and from this controlLyapunov function we construct a feedback
CONTROL LYAPUNOV FUNCTIONS FOR HOMOGENEOUS “JURDJEVICQUINN” SYSTEMS
, 2000
"... This paper presents a method to design explicit control Lyapunov functions for affine and homogeneous systems that satisfy the socalled “JurdjevicQuinn conditions”. For these systems a positive definite function V0 is known that can only be made non increasing by feedback. We describe how a cont ..."
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Cited by 14 (0 self)
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This paper presents a method to design explicit control Lyapunov functions for affine and homogeneous systems that satisfy the socalled “JurdjevicQuinn conditions”. For these systems a positive definite function V0 is known that can only be made non increasing by feedback. We describe how a
ControlLyapunov Functions For TimeVarying Set Stabilization
, 1997
"... This paper shows that, for time varying systems, global asymptotic controllability to a given closed subset of the state space is equivalent to the existence of a continuous controlLyapunov function with respect to the set. ..."
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Cited by 1 (0 self)
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This paper shows that, for time varying systems, global asymptotic controllability to a given closed subset of the state space is equivalent to the existence of a continuous controlLyapunov function with respect to the set.
Quadratic Control Lyapunov Functions for Bilinear Systems
, 1999
"... In this paper the existence of a quadratic control Lyapunov function for bilinear systems is considered. The existence of a control Lyapunov function ensures the existence of a control law which ensures the global asymptotic stability of the closed loop control system. In this paper we will derive c ..."
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In this paper the existence of a quadratic control Lyapunov function for bilinear systems is considered. The existence of a control Lyapunov function ensures the existence of a control law which ensures the global asymptotic stability of the closed loop control system. In this paper we will derive
Remarks on control lyapunov functions for discontinuous stabilizing feedback
 Proc. IEEE Conf. Decision and Control
, 1993
"... ABSTRACT We present a formula for a stabilizing feedback law under the assumption that a piecewise smooth controlLyapunov function exists. The resulting feedback is continuous at the origin and smooth everywhere except on a hypersurface of codimension 1. We provide an explicit and "univers ..."
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Cited by 10 (1 self)
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ABSTRACT We present a formula for a stabilizing feedback law under the assumption that a piecewise smooth controlLyapunov function exists. The resulting feedback is continuous at the origin and smooth everywhere except on a hypersurface of codimension 1. We provide an explicit and &
Results 1  10
of
102,145