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Computation of Piecewise Quadratic Lyapunov Functions for Hybrid Systems

by Mikael Johansson, Anders Rantzer - 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 ..."
Abstract - Cited by 259 (4 self) - Add to MetaCart
. 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

Properties of the Composite Quadratic Lyapunov Functions

by Tingshu Hu, Zongli Lin
"... Abstract—A composite quadratic Lyapunov function introduced re-cently was shown to be very useful in the study of set invariance properties for linear systems with input and state constraints and for systems with a class of convex/concave nonlinearities. In this note, more properties about this func ..."
Abstract - Cited by 2 (1 self) - Add to MetaCart
Abstract—A composite quadratic Lyapunov function introduced re-cently was shown to be very useful in the study of set invariance properties for linear systems with input and state constraints and for systems with a class of convex/concave nonlinearities. In this note, more properties about

On optimal quadratic Lyapunov functions for Polynomial Systems

by G. Chesi, A. Tesi, A. Vicino - IN 15 TH INT. SYMP. ON MATHEMATICAL THEORY OF NETWORKS AND SYSTEMS , 2002
"... The problem of estimating the Domain of Attraction (DA) of equilibria of polynomial systems is considered. Specifically, the computation of the quadratic Lyapunov function which maximizes the volume of the estimate is addressed. In order to solve this double non-convex optimization problem, a sem ..."
Abstract - Cited by 4 (0 self) - Add to MetaCart
The problem of estimating the Domain of Attraction (DA) of equilibria of polynomial systems is considered. Specifically, the computation of the quadratic Lyapunov function which maximizes the volume of the estimate is addressed. In order to solve this double non-convex optimization problem, a

On the Nonexistence of Quadratic Lyapunov Functions for Consensus Algorithms

by Alex Olshevsky, John N. Tsitsiklis , 2008
"... We provide an example proving that there exists no quadratic Lyapunov function for a certain class of linear agreement/consensus algorithms, a fact that had been numerically verified in [6]. We also briefly discuss sufficient conditions for the existence of such a Lyapunov function. ..."
Abstract - Cited by 18 (1 self) - Add to MetaCart
We provide an example proving that there exists no quadratic Lyapunov function for a certain class of linear agreement/consensus algorithms, a fact that had been numerically verified in [6]. We also briefly discuss sufficient conditions for the existence of such a Lyapunov function.

1 On the Nonexistence of Quadratic Lyapunov Functions for Consensus Algorithms

by Alex Olshevsky, John N. Tsitsiklis , 706
"... We provide an example proving that there exists no quadratic Lyapunov function for a certain class of linear agreement/consensus algorithms, a fact that had been numerically verified in [6]. We also briefly discuss sufficient conditions for the existence of such a Lyapunov function. I. ..."
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We provide an example proving that there exists no quadratic Lyapunov function for a certain class of linear agreement/consensus algorithms, a fact that had been numerically verified in [6]. We also briefly discuss sufficient conditions for the existence of such a Lyapunov function. I.

The Positivstellensatz and Nonexistence of Common Quadratic Lyapunov Functions

by John M. Davis, Geoffrey Eisenbarth
"... Abstract—We provide an algorithm for establishing the nonex-istence of a common quadratic Lyapunov function for switched LTI systems under arbitrary switching. We show that this nonex-istence question is equivalent to the emptiness of an associated semi-algebraic set. The celebrated Positivstellensa ..."
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Abstract—We provide an algorithm for establishing the nonex-istence of a common quadratic Lyapunov function for switched LTI systems under arbitrary switching. We show that this nonex-istence question is equivalent to the emptiness of an associated semi-algebraic set. The celebrated

A polynomial-time algorithm for determining quadratic Lyapunov functions for nonlinear systems

by L. Vandenberghe , S. Boyd , 1993
"... We consider nonlinear systems dx/dt =f(x(t)) where Df(x(t)) is known to lie in the convex hull of L matrices A1,... ,A L 2 R n n. For such systems, quadratic Lyapunov functions can be determined using convex programming techniques [1]. This paper describes an algorithm that either finds a quadratic ..."
Abstract - Cited by 5 (0 self) - Add to MetaCart
We consider nonlinear systems dx/dt =f(x(t)) where Df(x(t)) is known to lie in the convex hull of L matrices A1,... ,A L 2 R n n. For such systems, quadratic Lyapunov functions can be determined using convex programming techniques [1]. This paper describes an algorithm that either finds a quadratic

Computing optimal quadratic Lyapunov function for polynomial nonlinear systems via LMIs

by Graziano Chesi, Alberto Tesi, Antonio Vicino - in Proc. of the 15th IFAC World Congress , 2002
"... Abstract: The problem of estimating the domain of attraction (DA) of equilibria of polynomial systems is considered. Specifically, the computation of the quadratic Lyapunov function which maximizes the volume of the estimate is addressed. In order to solve this double non-convex optimization problem ..."
Abstract - Cited by 18 (0 self) - Add to MetaCart
Abstract: The problem of estimating the domain of attraction (DA) of equilibria of polynomial systems is considered. Specifically, the computation of the quadratic Lyapunov function which maximizes the volume of the estimate is addressed. In order to solve this double non-convex optimization

Composite quadratic Lyapunov functions for constrained control systems

by Tingshu Hu, Zongli Lin - IEEE Transactions on Automatic Control , 2003
"... The composite quadratic function based on a group of quadratic functions was introduced in our recent pa-per [7]. Some important properties of this Lyapunov function were revealed. We showed that this function is continuously differentiable and its level set is the con-vex hull of a group of ellipso ..."
Abstract - Cited by 23 (5 self) - Add to MetaCart
The composite quadratic function based on a group of quadratic functions was introduced in our recent pa-per [7]. Some important properties of this Lyapunov function were revealed. We showed that this function is continuously differentiable and its level set is the con-vex hull of a group

Absolute stability analysis of discretetime systems with composite quadratic Lyapunov functions

by Tingshu Hu, Zongli Lin - IEEE Trans. Automat. Contr , 2005
"... Abstract—A generalized sector bounded by piecewise linear functions was introduced in a previous paper for the purpose of reducing conservatism in absolute stability analysis of systems with nonlinearity and/or uncertainty. This paper will further en-hance absolute stability analysis by using the co ..."
Abstract - Cited by 11 (1 self) - Add to MetaCart
the composite quadratic Lyapunov function whose level set is the convex hull of a family of ellipsoids. The absolute stability analysis will be approached by characterizing absolutely contractively invariant (ACI) level sets of the composite quadratic Lyapunov functions. This objective will be achieved through
Results 1 - 10 of 12,086