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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
Properties of the Composite Quadratic Lyapunov Functions
"... Abstract—A composite quadratic Lyapunov function introduced recently 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 ..."
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Cited by 2 (1 self)
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Abstract—A composite quadratic Lyapunov function introduced recently 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
 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 nonconvex optimization problem, a sem ..."
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Cited by 4 (0 self)
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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 nonconvex optimization problem, a
On the Nonexistence of Quadratic Lyapunov Functions for Consensus Algorithms
, 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. ..."
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Cited by 18 (1 self)
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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.
1 On the Nonexistence of Quadratic Lyapunov Functions for Consensus Algorithms
, 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
"... Abstract—We provide an algorithm for establishing the nonexistence of a common quadratic Lyapunov function for switched LTI systems under arbitrary switching. We show that this nonexistence question is equivalent to the emptiness of an associated semialgebraic set. The celebrated Positivstellensa ..."
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Abstract—We provide an algorithm for establishing the nonexistence of a common quadratic Lyapunov function for switched LTI systems under arbitrary switching. We show that this nonexistence question is equivalent to the emptiness of an associated semialgebraic set. The celebrated
A polynomialtime algorithm for determining quadratic Lyapunov functions for nonlinear systems
, 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 ..."
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Cited by 5 (0 self)
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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
 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 nonconvex optimization problem ..."
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Cited by 18 (0 self)
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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 nonconvex optimization
Composite quadratic Lyapunov functions for constrained control systems
 IEEE Transactions on Automatic Control
, 2003
"... The composite quadratic function based on a group of quadratic functions was introduced in our recent paper [7]. Some important properties of this Lyapunov function were revealed. We showed that this function is continuously differentiable and its level set is the convex hull of a group of ellipso ..."
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Cited by 23 (5 self)
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The composite quadratic function based on a group of quadratic functions was introduced in our recent paper [7]. Some important properties of this Lyapunov function were revealed. We showed that this function is continuously differentiable and its level set is the convex hull of a group
Absolute stability analysis of discretetime systems with composite quadratic Lyapunov functions
 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 enhance absolute stability analysis by using the co ..."
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Cited by 11 (1 self)
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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
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12,086