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472
Quantized Feedback Stabilization of Linear Systems
 IEEE Trans. Automat. Control
, 2000
"... This paper addresses feedback stabilization problems for linear timeinvariant control systems with saturating quantized measurements. We propose a new control design methodology, which relies on the possibility of changing the sensitivity of the quantizer while the system evolves. The equation that ..."
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Cited by 293 (27 self)
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This paper addresses feedback stabilization problems for linear timeinvariant control systems with saturating quantized measurements. We propose a new control design methodology, which relies on the possibility of changing the sensitivity of the quantizer while the system evolves. The equation that describes the evolution of the sensitivity with time (discrete rather than continuous in most cases) is interconnected with the given system (either continuous or discrete), resulting in a hybrid system. When applied to systems that are stabilizable by linear timeinvariant feedback, this approach yields global asymptotic stability. Index TermsFeedback stabilization, hybrid system, linear control system, quantized measurement. I. INTRODUCTION T HIS PAPER deals with quantized feedback stabilization problems for linear timeinvariant control systems. A quantizer, as defined here, acts as a functional that maps a realvalued function into a piecewise constant function taking on a finite...
On Characterizations of the InputtoState Stability Property
 SYSTEMS CONTROL LETTERS
, 1995
"... We show that the wellknown Lyapunov sufficient condition for "inputtostate stability" is also necessary, settling positively an open question raised by several authors during the past few years. Additional characterizations of the ISS property, including one in terms of nonlinear stabil ..."
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Cited by 225 (32 self)
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We show that the wellknown Lyapunov sufficient condition for "inputtostate stability" is also necessary, settling positively an open question raised by several authors during the past few years. Additional characterizations of the ISS property, including one in terms of nonlinear stability margins, are also provided. 1 Introduction In practice, control systems are very often affected by noise, expressed for instance as perturbations on controls and errors on observations. Thus, it is desirable for a system not only to be stable, but also to display socalled "input/state" stability properties. Intuitively, this means that the behavior of the system should remain bounded when its inputs are bounded, and should tend to equilibrium when inputs tend to zero. These notions are closely related to the topic of stability under perturbations (total stability), studied in the classical dynamical systems literature. In the late 1980s, one of the coauthors introduced a particular precise defin...
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 196 (42 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 "universal" Construction Of Artstein's Theorem On Nonlinear Stabilization
 Systems & Control Letters
, 1989
"... This note presents an explicit proof of the theorem due to Artstein which states that the existence of a smooth controlLyapunov function implies smooth stabilizability. Moreover, the result is extended to the realanalytic and rational cases as well. The proof uses a "universal" formu ..."
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Cited by 177 (17 self)
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This note presents an explicit proof of the theorem due to Artstein which states that the existence of a smooth controlLyapunov function implies smooth stabilizability. Moreover, the result is extended to the realanalytic and rational cases as well. The proof uses a "universal" formula given by an algebraic function of Lie derivatives; this formula originates in the solution of a simple Riccati equation. Rutgers Center for Systems and Control February 1989 1 Keywords: Smooth stabilization, Artstein's Theorem. 2 Research supported in part by US Air Force Grant 880235 1 Introduction The main object of this note is to provide a simple, explicit, and in a sense "universal" proof of a result due to Artstein ([1]), and to obtain certain generalizations of it. The result concerns control systems of the type x(t) = f(x(t)) + u 1 (t)g 1 (x(t)) + : : : + um (t)g m (x(t)) (1) with states x(t) 2 IR n and controls u(t) = (u 1 (t); : : : ; um (t)) 2 IR m , where f as well as the ...
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 134 (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.
Comments on integral variants of ISS.
 Systems & Control Letters,
, 1998
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A general result on the stabilization of linear systems using bounded controls
 IEEE Transactions on Automatic Control
, 1994
"... We present two constructions of controllers that globally stabilize linear systems subject to control saturation. We allow essentially arbitrary saturation functions. The only conditions imposed on the system are the obvious necessary ones, namely that no eigenvalues of the uncontrolled system have ..."
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Cited by 103 (7 self)
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We present two constructions of controllers that globally stabilize linear systems subject to control saturation. We allow essentially arbitrary saturation functions. The only conditions imposed on the system are the obvious necessary ones, namely that no eigenvalues of the uncontrolled system have positive real part and that the standard stabilizability rank condition hold. One of the constructions is in terms of a ”neuralnetwork type ” onehidden layer architecture, while the other one is in terms of cascades of linear maps and saturations.
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 96 (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 Lyapunov Formulation of Nonlinear Small Gain Theorem for Interconnected ISS Systems
, 1996
"... The goal of this paper is to provide a Lyapunov statement and proof of the recent nonlinear smallgain theorem for interconnected input/state stable (iss) systems. An issLyapunov function for the overall system is obtained from the corresponding Lyapunov functions for both the subsystems. ..."
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Cited by 95 (13 self)
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The goal of this paper is to provide a Lyapunov statement and proof of the recent nonlinear smallgain theorem for interconnected input/state stable (iss) systems. An issLyapunov function for the overall system is obtained from the corresponding Lyapunov functions for both the subsystems.