Results 1 - 10 of 102,145

Nonsmooth Control-Lyapunov Functions

by Eduardo Sontag, Héctor J. Sussmann - 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 set-va ..."
Abstract - Cited by 42 (7 self) - Add to MetaCart
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

by M. Lazar - 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 closed-loop state trajectory is contained within a cone with a fixed, predefined shape, and which is centered at and ..."
Abstract - Cited by 7 (7 self) - Add to MetaCart
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 closed-loop state trajectory is contained within a cone with a fixed, predefined shape, and which is centered

Smooth patchy control Lyapunov functions

by Rafal Goebel, et al. , 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 ..."
Abstract - Cited by 7 (2 self) - Add to MetaCart
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 Control-Lyapunov Functions

by Eduardo D. Sontag, Héctor J. SUSSMANN , 1995
"... The main result of this paper establishes the equivalence between null asymptotic controllability of nonlinear finite-dimensional control systems and the existence of continuous control-Lyapunov functions (clf's) defined by means of generalized derivatives. In this manner, one obtains a compl ..."
Abstract - Cited by 3 (0 self) - Add to MetaCart
The main result of this paper establishes the equivalence between null asymptotic controllability of nonlinear finite-dimensional control systems and the existence of continuous control-Lyapunov functions (clf's) defined by means of generalized derivatives. In this manner, one obtains a

LOWER BOUNDED CONTROL-LYAPUNOV FUNCTIONS ∗

by Ronald Hirschorn
"... 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 control-Lyapunov function from which it is po ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
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 control-Lyapunov function from which

Weak converse Lyapunov theorems and control Lyapunov functions

by Christopher M. Kellett, Andrew, R. Teel - 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 ..."
Abstract - Cited by 10 (2 self) - Add to MetaCart
. 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 control-Lyapunov function, and from this control-Lyapunov function we construct a feedback

CONTROL LYAPUNOV FUNCTIONS FOR HOMOGENEOUS “JURDJEVIC-QUINN” SYSTEMS

by ludovic faubourg, jean-baptiste pomet , 2000
"... This paper presents a method to design explicit control Lyapunov functions for affine and homogeneous systems that satisfy the so-called “Jurdjevic-Quinn 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 ..."
Abstract - Cited by 14 (0 self) - Add to MetaCart
This paper presents a method to design explicit control Lyapunov functions for affine and homogeneous systems that satisfy the so-called “Jurdjevic-Quinn conditions”. For these systems a positive definite function V0 is known that can only be made non increasing by feedback. We describe how a

Control-Lyapunov Functions For Time-Varying Set Stabilization

by Francesca Albertini, Eduardo D. Sontag , 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 control-Lyapunov function with respect to the set. ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
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 control-Lyapunov function with respect to the set.

Quadratic Control Lyapunov Functions for Bilinear Systems

by Bernd Tibken, Frank Lehn, Eberhard P. Hofer , 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 ..."
Abstract - Add to MetaCart
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

by G. A. Lafferriere, Eduardo D. Sontag - Proc. IEEE Conf. Decision and Control , 1993
"... ABSTRACT We present a formula for a stabilizing feedback law under the assumption that a piecewise smooth control-Lyapunov 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 ..."
Abstract - Cited by 10 (1 self) - Add to MetaCart
ABSTRACT We present a formula for a stabilizing feedback law under the assumption that a piecewise smooth control-Lyapunov 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