Results 1  10
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24
Connectivity in AdHoc and Hybrid Networks
 IN PROC. IEEE INFOCOM
, 2002
"... We consider a largescale wireless network, but with a low density of nodes per unit area. Interferences are then less critical, contrary to connectivity. This paper studies the latter property for both a purely adhoc network and a hybrid network, where fixed base stations can be reached in multipl ..."
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Cited by 160 (6 self)
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We consider a largescale wireless network, but with a low density of nodes per unit area. Interferences are then less critical, contrary to connectivity. This paper studies the latter property for both a purely adhoc network and a hybrid network, where fixed base stations can be reached in multiple hops. We assume here that power constraints are modeled by a maximal distance above which two nodes are not (directly) connected. We find that
A Smooth Converse Lyapunov Theorem for Robust Stability
 SIAM Journal on Control and Optimization
, 1996
"... . This paper presents a Converse Lyapunov Function Theorem motivated by robust control analysis and design. Our result is based upon, but generalizes, various aspects of wellknown classical theorems. In a unified and natural manner, it (1) allows arbitrary bounded timevarying parameters in the sys ..."
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Cited by 143 (44 self)
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. This paper presents a Converse Lyapunov Function Theorem motivated by robust control analysis and design. Our result is based upon, but generalizes, various aspects of wellknown classical theorems. In a unified and natural manner, it (1) allows arbitrary bounded timevarying parameters in the system description, (2) deals with global asymptotic stability, (3) results in smooth (infinitely differentiable) Lyapunov functions, and (4) applies to stability with respect to not necessarily compact invariant sets. 1. Introduction. This work is motivated by problems of robust nonlinear stabilization. One of our main contributions is to provide a statement and proof of a Converse Lyapunov Function Theorem which is in a form particularly useful for the study of such feedback control analysis and design problems. We provide a single (and natural) unified result that: 1. applies to stability with respect to not necessarily compact invariant sets; 2. deals with global (as opposed to merely loca...
A smooth Lyapunov function from a classKL estimate involving two positive semidefinite functions
 ESAIM, Control Optim. Calc. Var
, 2000
"... Abstract. We consider differential inclusions where a positive semidefinite function of the solutions satisfies a classKL estimate in terms of time and a second positive semidefinite function of the initial condition. We show that a smooth converse Lyapunov function, i.e., one whose derivative alon ..."
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Cited by 41 (11 self)
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Abstract. We consider differential inclusions where a positive semidefinite function of the solutions satisfies a classKL estimate in terms of time and a second positive semidefinite function of the initial condition. We show that a smooth converse Lyapunov function, i.e., one whose derivative along solutions can be used to establish the classKL estimate, exists if and only if the classKL estimate is robust, i.e., it holds for a larger, perturbed differential inclusion. It remains an open question whether all classKL estimates are robust. One sufficient condition for robustness is that the original differential inclusion is locally Lipschitz. Another sufficient condition is that the two positive semidefinite functions agree and a backward completability condition holds. These special cases unify and generalize many results on converse Lyapunov theorems for differential equations and differential inclusions that have appeared in the literature. AMS Subject Classification. 34A60, 34D20, 34B25.
Adaptive Lexicographic Optimization in MultiClass M/GI/1 Queues
 Mathematics of Operations Research
, 1993
"... this paper we take a di#erent approach. While the choice of cost function for a particular system is often ad hoc, it is more natural to associate an average response time objective with each class and consider its performance relative to the objective. Specically, let # # be the response time objec ..."
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Cited by 5 (2 self)
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this paper we take a di#erent approach. While the choice of cost function for a particular system is often ad hoc, it is more natural to associate an average response time objective with each class and consider its performance relative to the objective. Specically, let # # be the response time objective and let # denote the longrun average response time (assuming it exists) of class # customers under a scheduling policy #. Attention is restricted to the class # of nonidling, nonpreemptive, and nonanticipative policies; the last term means that scheduling decisions do not depend on future arrival and service times. We are interested in determining a policy in # which lexicographically minimizes the vector of performance ratios ( 1 ## 1 ##### # ## # ) # (1) arranged in nonincreasing order (see Section 2 for the denition.) We will refer to this minimization as lexicographic. Results on optimality crucially hinge on the possibility of characterizing the subset of ## that consists of the vectors of mean response times achievable by policies in #.ThesetA is known to be the base of a polymatroid and is described in Section 2. The lexicographic minimization of vector (1)overthesetA yields a unique point # # := (# # 1 ## 1 ###### # # ## # ) .Suchapointhas certain properties that capture fairness in resource allocation. These are described in remarks following Problem (P) of Section 2. Lexicographic minimization has been studied extensively in a deterministic context [15], [23]. The main contribution of this paper is two simple adaptive policies that (exactly and approximately, respectively) minimize (1) lexicographically. Three quantities are needed in order to specify our policies. Set # 0 =0and denote by # # the end of the #th busy period, # =1# 2##...
PROPOSITIONS on the ROBUSTNESS of MULTISTEP FORMULAE
 J. Numer. Func. Anal. Optim
, 1994
"... Classical analysis of linear multistep formulae (LMFs) for initialvalue problems in ordinary differential equations (ODEs) has concentrated on problems satisfying uniform Lipschitz or onesided Lipschitz conditions, and corresponding stability models. We here contribute insight into the robustness ..."
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Cited by 3 (3 self)
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Classical analysis of linear multistep formulae (LMFs) for initialvalue problems in ordinary differential equations (ODEs) has concentrated on problems satisfying uniform Lipschitz or onesided Lipschitz conditions, and corresponding stability models. We here contribute insight into the robustness of such formulae for equations with a stronger nonlinearity and of related formulae for functional differential equations y 0 (t) = \Phi ` y(t); y(t \Gamma ); Z t 0 K(t \Gamma s)g(y(s)) ds ' : Key words. Linear multistep formulae, nonlinear dynamics, stability, delaydifferential equations, Volterra integral & integrodifferential equations. AMS subject classifications. primary 65L05, 65L06, 65L20, 65R99 1 Introduction: Some evolutionary problems Our discussion relates to constant stepsize numerical formulae for various functional equations. We indicate the variety of functional equations and outline the range of numerical formulae later. 1.1 Functional differential equations Ou...
A Higher Order Local Linearization Method for Solving Ordinary Differential Equations
"... The Local Linearization (LL) method for the integration of ordinary differential equations is an explicit onestep method that has a number of suitable dynamical properties. However, a major drawback of the LL integrator is that its order of convergence is only two. The present paper overcomes this ..."
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Cited by 3 (0 self)
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The Local Linearization (LL) method for the integration of ordinary differential equations is an explicit onestep method that has a number of suitable dynamical properties. However, a major drawback of the LL integrator is that its order of convergence is only two. The present paper overcomes this limitation by introducing a new class of numerical integrators, called the LLT method, that is based on the addition of a correction term to the LL approximation. In this way an arbitrary order of convergence can be achieved while retaining the dynamic properties of the LL method. In particular, it is proved that the LLT method reproduces correctly the phase portrait of a dynamical system near hyperbolic stationary points to the order of convergence. The performance of the introduced method is further illustrated through computer simulations.
A converse Lyapunov theorem and inputtostate stability properties for discretetime nonlinear systems
"... In this work we study the inputtostate stability (ISS) property for discretetime nonlinear systems. We first establish a converse Lyapunov theorem for robust global asymptotic stability in discretetime. Then, it is shown that most iss results for continuoustime nonlinear systems in the current ..."
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Cited by 2 (0 self)
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In this work we study the inputtostate stability (ISS) property for discretetime nonlinear systems. We first establish a converse Lyapunov theorem for robust global asymptotic stability in discretetime. Then, it is shown that most iss results for continuoustime nonlinear systems in the current literature can be extended to the discretetime case. Several equivalent characterizations of iss are introduced and two iss smallgain theorems are proved for nonlinear and interconnected discretetime systems. ISS stabilizability is discussed and comparisons with the continuoustime case are made. As in the continuous time framework, where the notion iss found wide applications, we expect that this notion will provide a useful tool in areas related to stability and stabilization for nonlinear discrete time systems as well.
Asymptotic Stability Of Nonlinear Control Systems Described By Difference Equations With Multiple Delays
, 2000
"... . In this paper we study nonlinear control systems with multiple delays on controls and states. To obtain asymptotic stability, we impose Holdertype assumptions on the perturbing function, and show a Gronwalltype inequality for di#erence equations with delay. We prove that a nonlinear control syst ..."
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Cited by 1 (0 self)
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. In this paper we study nonlinear control systems with multiple delays on controls and states. To obtain asymptotic stability, we impose Holdertype assumptions on the perturbing function, and show a Gronwalltype inequality for di#erence equations with delay. We prove that a nonlinear control system can be stabilized if its linear control system can be stabilized. Some examples are included in the last part of this paper. 1. Introduction Consider a nonlinear control system described by discretetime equations, with multiple delays on the controls and states, of the form x(k +1)=L p,q (x k ,u k)+f p,q (k, x k ,u k) ,k#Z + , (1) where L p,q (x k ,u k)= p # j=1 A j (k)x(k  p j )+ q # i=1 B i (k)u(k  q i ), f p,q (k, x k ,u k)=f( k, x(k  p 1 ),x(kp 2 ),...,x(kp p ),u(kq 1 ), .., u(k  q q )), Z + := {0, 1, 2,...}, x(k)#R n , u(k)#R m with n # m, A j (k)andB i (k)arenn and n m matrices with k # Z + , f (k, .):Z + R pn R qm # R n with p, q # 1, q q # p p...
Departments Of Mathematics
"... June 1996 saw two meetings to mark the centennial of the mathematical work of Vito Volterra, the first being held at the University of Texas at Arlington (organised by Professors Corduneanu and Kanner) and the second at the State University of Arizona at Tempe. In invited talks at each meeting, the ..."
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June 1996 saw two meetings to mark the centennial of the mathematical work of Vito Volterra, the first being held at the University of Texas at Arlington (organised by Professors Corduneanu and Kanner) and the second at the State University of Arizona at Tempe. In invited talks at each meeting, the firstnamed author presented joint work that follows, in chronological sequence, in this technical report. Christopher T H Baker & Arslang Tang 2 GENERALIZED HALANAY INEQUALITIES FOR VOLTERRA FUNCTIONAL DIFFERENTIAL EQUATIONS AND DISCRETIZED VERSIONS CHRISTOPHER T.H. BAKER 1 & ARSALANG TANG 2 Department of Pure and Applied Mathematics, The Victoria University of Manchester, England Abstract. Halanay's inequality provides a decreasing bound on a function satisfying a delaydifferential inequality, subject to certain conditions, and it has been used by Halanay to analyze asymptotic stability of the zero solution of a certain delaydifferential equations with fixed lag. The original ineq...