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Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization
, 2000
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InputToState Stability For DiscreteTime Nonlinear Systems
 Automatica
, 1999
"... : In this paper the inputtostate stability (iss) property is studied for discretetime nonlinear systems. We show that many iss results for continuoustime nonlinear systems in earlier papers (Sontag, 1989; Sontag, 1990; Sontag and Wang, 1996; Jiang et al., 1994; Coron et al., 1995) can be exten ..."
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Cited by 144 (9 self)
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: In this paper the inputtostate stability (iss) property is studied for discretetime nonlinear systems. We show that many iss results for continuoustime nonlinear systems in earlier papers (Sontag, 1989; Sontag, 1990; Sontag and Wang, 1996; Jiang et al., 1994; Coron et al., 1995) can be extended to the discretetime case. More precisely, we provide a Lyapunovlike su#cient condition for iss, and we show the equivalence between the iss property and various other properties. Utilizing the notion of iss, we present a small gain theorem for nonlinear discrete time systems. ISS stabilizability is discussed and connections with the continuoustime case are made. As in the continuous time case, where the notion iss found wide applications, we expect that this notion will provide a useful tool in areas related to stability for nonlinear discrete time systems as well. Keywords: discretetime nonlinear systems, inputtostate stability, Lyapunov methods. 1. INTRODUCTION The notio...
Leadertoformation stability
 IEEE Transactions on Robotics and Automation
, 2004
"... Abstract—The paper investigates the stability properties of mobile agent formations which are based on leaderfollowing. We derive nonlinear gain estimates that capture how leader behavior affects the interconnection errors observed in the formation. Leader to formation stability (LFS) gains quantif ..."
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Cited by 133 (6 self)
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Abstract—The paper investigates the stability properties of mobile agent formations which are based on leaderfollowing. We derive nonlinear gain estimates that capture how leader behavior affects the interconnection errors observed in the formation. Leader to formation stability (LFS) gains quantify error ampli£cation, relate interconnection topology to stability and performance and offer safety bounds for different formation topologies. Analysis based on the LFS gains provides insight to error propagation and suggests ways to improve the safety, robustness and performance characteristics of a formation. I.
A control Lyapunov function approach to multiagent coordination,” presented at the
 IEEE Conf. Decision and Control
, 2001
"... Abstract—In this paper, the multiagent coordination problem is studied. This problem is addressed for a class of robots for which control Lyapunov functions can be found. The main result is a suite of theorems about formation maintenance, task completion time, and formation velocity. It is also show ..."
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Cited by 117 (2 self)
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Abstract—In this paper, the multiagent coordination problem is studied. This problem is addressed for a class of robots for which control Lyapunov functions can be found. The main result is a suite of theorems about formation maintenance, task completion time, and formation velocity. It is also shown how to moderate the requirement that, for each individual robot, there exists a control Lyapunov function. An example is provided that illustrates the soundness of the method. Index Terms—Coordinated control, Lyapunov methods, mobile robots, multirobot system, robot formation control.
Asymptotic Controllability Implies Feedback Stabilization
 IEEE Trans. Autom. Control
, 1999
"... It is shown that every asymptotically controllable system can be globally stabilized by means of some (discontinuous) feedback law. The stabilizing strategy is based on pointwise optimization of a smoothed version of a controlLyapunov function, iteratively sending trajectories into smaller and smal ..."
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Cited by 117 (11 self)
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It is shown that every asymptotically controllable system can be globally stabilized by means of some (discontinuous) feedback law. The stabilizing strategy is based on pointwise optimization of a smoothed version of a controlLyapunov function, iteratively sending trajectories into smaller and smaller neighborgoods of a desired equilibrium. A major technical problem, and one of contributions of the present paper, concerns the precise meaning of "solution" when using a discontinuous controller. I. Introduction A longstanding open question in nonlinear control theory concerns the relationship between asymptotic controllability to the origin in R n of a nonlinear system x = f(x; u) (1) by an "open loop" control u : [0; +1) ! U and the existence of a feedback control k : R n ! U which stabilizes trajectories of the system x = f(x; k(x)) (2) with respect to the origin. For the special case of linear control systems x = Ax + Bu, this relationship is well understood: asymptotic cont...
A Lyapunov approach to incremental stability
"... . This paper deals with several notions of incremental stability. In other words, we focus on stability of trajectories with respect to one another, rather than with respect some attractor or equilibrium point. The aim is to present a framework for understanding such questions fully compatible with ..."
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Cited by 110 (2 self)
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. This paper deals with several notions of incremental stability. In other words, we focus on stability of trajectories with respect to one another, rather than with respect some attractor or equilibrium point. The aim is to present a framework for understanding such questions fully compatible with the wellknown InputtoState Stability approach. 1 Introduction InputtoState stability (### for short) has proven a valid instrument in order to study questions of robust stability for nitedimensional nonlinear systems. One reason for that is the possibility of dealing at the same time with a body of theory which nicely extends the classic Lyapunov approach to nonautonomous systems, while still allowing for inputoutput descriptions of the system behavior [15]. In this way tools such as smallgain theorems and Lyapunov dissipation inequalities [1, 13] have come together in a unied framework which bridges the gap between the statespace and inputoutput approaches. Stability propertie...
Comments on integral variants of ISS.
 Systems & Control Letters,
, 1998
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High performance adaptive robust control of nonlinear systems: A general framework and new schemes
 Proceedings of the 36th Conference on Decision and Control
, 1997
"... A general framework is proposed for the design of a new class of highperformance robust controllers. The framework is based on the recently proposed adaptive robust control (ARC), which effectively combines deterministic robust control with adaptive control. The approach intends to use all availabl ..."
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Cited by 95 (48 self)
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A general framework is proposed for the design of a new class of highperformance robust controllers. The framework is based on the recently proposed adaptive robust control (ARC), which effectively combines deterministic robust control with adaptive control. The approach intends to use all available means in achieving high performance; robust filter structures are used to attenuate the effect of model uncertainties as much as possible while learning mechanisms such as parameter adaptation are used to reduce the model uncertainties. Under the proposed general framework, a simple new ARC controller is also constructed for a class of nonlinear systems transformable to a semistrict feedback form. The new design utilizes the popular discontinuous projection method in solving the conflicts between the deterministic robust control design and the adaptive control design, which is much simpler than the smooth projection or the smooth modifications of adaptation law used in the previously proposed ARC controllers. The controller achieves a guaranteed transient performance and a prescribed final tracking accuracy in the presence of both parametric uncertainties and uncertain nonlinearities while achieving asymptotic stability in the presence of parametric uncertainties without using a discontinuous control law or infinitegain feedback. 1
Input to state stability: Basic concepts and results
 Nonlinear and Optimal Control Theory
, 2006
"... The analysis and design of nonlinear feedback systems has recently undergone an exceptionally rich period of progress and maturation, fueled, to a great extent, by (1) the discovery of certain basic conceptual notions, and (2) the identification of classes of systems for which systematic decompositi ..."
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Cited by 95 (6 self)
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The analysis and design of nonlinear feedback systems has recently undergone an exceptionally rich period of progress and maturation, fueled, to a great extent, by (1) the discovery of certain basic conceptual notions, and (2) the identification of classes of systems for which systematic decomposition approaches can result in effective
A characterization of integral inputtostate stability
 IEEE Trans. Autom. Control
, 2000
"... AbstractThe notion of inputtostate stability (ISS) is now recognized as a central concept in nonlinear systems analysis. It provides a nonlinear generalization of finite gains with respect to supremum norms and also of finite 2 gains. It plays a central role in recursive design, coprime factoriz ..."
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Cited by 87 (10 self)
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AbstractThe notion of inputtostate stability (ISS) is now recognized as a central concept in nonlinear systems analysis. It provides a nonlinear generalization of finite gains with respect to supremum norms and also of finite 2 gains. It plays a central role in recursive design, coprime factorizations, controllers for nonminimum phase systems, and many other areas. In this paper, a newer notion, that of integral inputtostate stability (iISS), is studied. The notion of iISS generalizes the concept of finite gain when using an integral norm on inputs but supremum norms of states, in that sense generalizing the linear " 2 " theory. It allows one to quantify sensitivity even in the presence of certain forms of nonlinear resonance. We obtain here several necessary and sufficient characterizations of the iISS property, expressed in terms of dissipation inequalities and other alternative and nontrivial characterizations. These characterizations serve to show that integral inputtostate stability is a most natural concept, one that might eventually play a role at least comparable to, if not even more important than, ISS.