Results 1  10
of
28
InputOutputtoState Stability
 SIAM J. Control Optim
, 1999
"... This work explores Lyapunov characterizations of the inputoutputtostate stability (oss) property for nonlinear systems. The notion of IOSS is a natural generalization of the standard zerodetectability property used in the linear case. The main contribution of this work is to establish a compl ..."
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Cited by 44 (18 self)
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This work explores Lyapunov characterizations of the inputoutputtostate stability (oss) property for nonlinear systems. The notion of IOSS is a natural generalization of the standard zerodetectability property used in the linear case. The main contribution of this work is to establish a complete equivalence between the inputoutputtostate stability property and the existence of a certain type of smooth Lyapunov function. As corollaries, one shows the existence of "normestimators", and obtains characterizations of nonlinear detectability in terms of relative stability and of finiteenergy estimates.
Results on inputtostate stability for hybrid systems
, 2005
"... We show that, like continuoustime systems, zeroinput locally asymptotically stable hybrid systems are locally inputtostatestable (LISS). We demonstrate by examples that, unlike continuoustime systems, zeroinput locally exponentially stable hybrid systems may not be LISS with linear gain, inpu ..."
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Cited by 14 (2 self)
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We show that, like continuoustime systems, zeroinput locally asymptotically stable hybrid systems are locally inputtostatestable (LISS). We demonstrate by examples that, unlike continuoustime systems, zeroinput locally exponentially stable hybrid systems may not be LISS with linear gain, inputtostate stable (ISS) hybrid systems may not admit any ISS Lyapunov function, and nonuniform ISS hybrid systems may not be (uniformly) ISS. We then provide a strengthened ISS condition as an equivalence to the existence of an ISS Lyapunov function for hybrid systems. This strengthened condition reduces to standard ISS for continuoustime and discretetime systems. Finally under some other assumptions we establish the equivalence among ISS, several asymptotic characterizations of ISS, and the existence of an ISS Lyapunov function for hybrid systems.
A smallgain theorem with applications to input/output systems, incremental stability, detectability, and interconnections
 Journal of the Franklin Institute
, 2002
"... Abstract A general ISStype smallgain result is presented. It specializes to a smallgain theorem for ISS operators, and it also recovers the classical statement for ISS systems in statespace form. In addition, we highlight applications to incrementally stable systems, detectable systems, and to i ..."
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Cited by 11 (3 self)
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Abstract A general ISStype smallgain result is presented. It specializes to a smallgain theorem for ISS operators, and it also recovers the classical statement for ISS systems in statespace form. In addition, we highlight applications to incrementally stable systems, detectable systems, and to interconnections of stable systems.
A passivitybased stability criterion for a class of interconnected systems and applications to biochemical reaction networks
 Mathematical Biosciences and Engineering
, 2007
"... (Communicated by Sergei Pilyugin) Abstract. This paper presents a stability test for a class of interconnected nonlinear systems motivated by biochemical reaction networks. The main result determines global asymptotic stability of the network from the diagonal stability of a dissipativity matrix whi ..."
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Cited by 10 (4 self)
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(Communicated by Sergei Pilyugin) Abstract. This paper presents a stability test for a class of interconnected nonlinear systems motivated by biochemical reaction networks. The main result determines global asymptotic stability of the network from the diagonal stability of a dissipativity matrix which incorporates information about the passivity properties of the subsystems, the interconnection structure of the network, and the signs of the interconnection terms. This stability test encompasses the secant criterion for cyclic networks presented in [1], and extends it to a general interconnection structure represented by a graph. The new stability test is illustrated on a mitogenactivated protein kinase (MAPK) cascade model, and on a branched interconnection structure motivated by metabolic networks. The next problem addressed is the robustness of stability in the presence of diffusion terms. A compartmental model is used to represent the localization of the reactions, and conditions are presented under which stability is preserved despite the diffusion terms between the compartments.
Stability Properties of Interconnected Vehicles
 in 15th International Symposium on Mathematical Theory of Networks and Systems, South
, 2002
"... The paper presents a methodology for analyzing the stability of formations of interconnected vehicles that are based on leaderfollower relations. The methodology exploits inputtostate stability properties of basic leaderfollower interconnections and builds on the propagation of these properti ..."
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Cited by 8 (2 self)
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The paper presents a methodology for analyzing the stability of formations of interconnected vehicles that are based on leaderfollower relations. The methodology exploits inputtostate stability properties of basic leaderfollower interconnections and builds on the propagation of these properties throughout the network to establish global stability bounds. This is formalized using the notion of (formation ISS),aweakerform of stability than string or mesh stability, which relates leader input(s) to formation state errors. In this paper we focus on cyclic interconnections of vehicles and show how the ISS framework can be extended to include these structures. This is the first such result for cyclic graphs that represent formations based on leaderfollower controllers.
Inversion in indirect optimal control of multivariable systems
 ESAIM: CONTROL, OPTIMISATION AND CALCULUS OF VARIATIONS
, 2008
"... This paper presents the role of vector relative degree in the formulation of stationarity conditions of optimal control problems for affine control systems. After translating the dynamics into a normal form, we study the Hamiltonian structure. Stationarity conditions are rewritten with a limited num ..."
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Cited by 4 (3 self)
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This paper presents the role of vector relative degree in the formulation of stationarity conditions of optimal control problems for affine control systems. After translating the dynamics into a normal form, we study the Hamiltonian structure. Stationarity conditions are rewritten with a limited number of variables. The approach is demonstrated on two and three inputs systems, then, we prove a formal result in the general case. A mechanical system example serves as illustration.
A Constructive Proof of ISS SmallGain Theorem Using Generalized Scaling
, 2002
"... This paper presents a Lyapunovtype proof of the InputtoState Stable(ISS) smallgain theorem. The proof given in this paper demonstrates how to construct a Lyapunov function explicitly, which contrasts with existing proofs based on inputoutput analysis. The Lyapunov functions are constructed by s ..."
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Cited by 4 (1 self)
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This paper presents a Lyapunovtype proof of the InputtoState Stable(ISS) smallgain theorem. The proof given in this paper demonstrates how to construct a Lyapunov function explicitly, which contrasts with existing proofs based on inputoutput analysis. The Lyapunov functions are constructed by selecting statedependent scaling functions properly. The construction of Lyapunov functions motivates the author to formulate a new criterion for stability and performance of interconnected nonlinear systems. Furthermore, an ISS smallgain condition with nonlinearlyscaled supply rates is obtained naturally in order to reduce the conservatism arising in the application of the ISS smallgain condition.
Output Stabilization via Nonlinear Luenberger Observers ∗
, 2006
"... The present paper addresses the problem of existence of an (output) feedback law to the purposes of asymptotically steering to zero a given controlled variable, while keeping all state variables bounded, for any initial conditions in a given compact set. The problem can be viewed as an extension of ..."
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Cited by 2 (1 self)
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The present paper addresses the problem of existence of an (output) feedback law to the purposes of asymptotically steering to zero a given controlled variable, while keeping all state variables bounded, for any initial conditions in a given compact set. The problem can be viewed as an extension of the classical problem of semiglobally stabilizing the trajectories of a controlled system to a compact set. The problem also encompasses a version of the classical problem of output regulation. Assuming only the existence of a feedback law that keeps the trajectories of the zero dynamics of the controlled plant bounded, it is shown that there exists a controller solving the problem at hand. The paper is deliberately focused on theoretical results regarding the existence of such controller. Practical aspects involving the design and the implementation of the controller are left to a forthcoming work.