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Notions of Input to Output Stability  [PDF]
Eduardo D. Sontag,Y. Wang
Mathematics , 1999,
Abstract: This paper deals with several related notions of output stability with respect to inputs. The inputs may be thought of as disturbances; when there are no inputs, one obtains generalizations of the classical concepts of partial stability. The main notion studied is called input to output stability (IOS), and it reduces to input to state stability (ISS) when the output equals the complete state. Several variants, which formalize in different manners the transient behavior, are introduced. The main results provide a comparison among these notions. A companion paper establishes necessary and sufficient Lyapunov-theoretic characterizations.
Input-Output-to-State Stability  [PDF]
Mikhail Krichman,Eduardo D. Sontag,Yuan Wang
Mathematics , 1999,
Abstract: This work explores Lyapunov characterizations of the input-output-to-state stability (IOSS) property for nonlinear systems. The notion of IOSS is a natural generalization of the standard zero-detectability property used in the linear case. The main contribution of this work is to establish a complete equivalence between the input-output-to-state stability property and the existence of a certain type of smooth Lyapunov function. As corollaries, one shows the existence of ``norm-estimators'', and obtains characterizations of nonlinear detectability in terms of relative stability and of finite-energy estimates.
Input-to-output stability properties of switched perturbed nonlinear control systems
Mancilla-Aguilar,J.L.; Garcia,R.A.;
Latin American applied research , 2009,
Abstract: in this paper we obtain the extension of results on input-to-output stability properties of switched systems to switched systems whose dynamics are described by perturbed forced differential equations and whose outputs are obtained via switched perturbed functions. we also present lyapunov characterizations of these input-output stability properties, obtained in terms of certain conceptual output functions.
Input-to-output stability properties of switched perturbed nonlinear control systems
J.L. Mancilla-Aguilar,R.A. Garcia
Latin American applied research , 2009,
Abstract: In this paper we obtain the extension of results on input-to-output stability properties of switched systems to switched systems whose dynamics are described by perturbed forced differential equations and whose outputs are obtained via switched perturbed functions. We also present Lyapunov characterizations of these input-output stability properties, obtained in terms of certain conceptual output functions.
Stability Results for Systems Described by Retarded Functional Differential Equations  [PDF]
Iasson Karafyllis,Pierdomenico Pepe,Zhong-Ping Jiang
Mathematics , 2006,
Abstract: In this work characterizations of notions of output stability for uncertain time-varying systems described by retarded functional differential equations are provided. Particularly, characterizations by means of Lyapunov and Razumikhin functions of uniform and non-uniform in time Robust Global Asymptotic Output Stability and Input-to-Output Stability are given. The results of this work have been developed for systems with outputs in abstract normed linear spaces in order to allow outputs with no delay, with discrete or distributed delay or functional outputs with memory.
Stability Results for Systems Described by Coupled Retarded Functional Differential Equations and Functional Difference Equations  [PDF]
Iasson Karafyllis,Pierdomenico Pepe,Zhong-Ping Jiang
Mathematics , 2007,
Abstract: In this work stability results for systems described by coupled Retarded Functional Differential Equations (RFDEs) and Functional Difference Equations (FDEs) are presented. The results are based on the observation that the composite system can be regarded as the feedback interconnection of a subsystem described by RFDEs and a subsystem described by FDEs. Recent Small-Gain results and Lyapunov-like characterizations of the Weighted Input-to-Output Stability property for systems described by RFDEs and FDEs are employed. It is shown that the stability results provided in this work can be used to study stability for systems described by neutral functional differential equations and systems described by hyperbolic partial differential equations.
Integral-Input-Output to State Stability  [PDF]
Brian Ingalls
Mathematics , 2001,
Abstract: A notion of detectability for nonlinear systems is discussed. Within the framework of ``input to state stability'' (ISS), a dual notion of ``output to state stability'' (OSS), and a more complete detectability notion, ``input-output to state stability'' (IOSS) have appeared in the literature. This note addresses a variant of the IOSS property, using an integral norm to measure signals, as opposed to the standard supremum norm that appears in ISS theory.
Input-Output Finite-Time Stability  [PDF]
Gianmaria De Tommasi,Roberto Ambrosino,Giuseppe Carannante,Carlo Cosentino,Alfredo Pironti,Francesco Amato
Mathematics , 2011,
Abstract: This paper introduces the extension of Finite-Time Stability (FTS) to the input-output case, namely the Input-Output FTS (IO-FTS). The main differences between classic IO stability and IO-FTS are that the latter involves signals defined over a finite time interval, does not necessarily require the inputs and outputs to belong to the same class of signals, and that quantitative bounds on both inputs and outputs must be specified. This paper revises some recent results on IO-FTS, both in the context of linear systems and in the context of switching systems. In the final example the proposed methodology is used to minimize the maximum displacement and velocity of a building subject to an earthquake of given magnitude.
On the output-input stability property for multivariable nonlinear control systems  [PDF]
Daniel Liberzon
Mathematics , 2002,
Abstract: We study the recently introduced notion of output-input stability, which is a robust variant of the minimum-phase property for general smooth nonlinear control systems. The subject of this paper is developing the theory of output-input stability in the multi-input, multi-output setting. We show that output-input stability can be viewed as a combination of two system properties, one related to detectability and the other to left-invertibility. For systems affine in controls, we provide a necessary and sufficient condition for output-input stability, which relies on Hirschorn's nonlinear structure algorithm.
Multi-Stability in Monotone Input/Output Systems  [PDF]
David Angeli,Eduardo D. Sontag
Quantitative Biology , 2003,
Abstract: This paper studies the emergence of multi-stability and hysteresis in those systems that arise, under positive feedback, starting from monotone systems with well-defined steady-state responses. Such feedback configurations appear routinely in several fields of application, and especially in biology. Characterizations of global stability behavior are stated in terms of easily checkable graphical conditions. An example of a signaling cascade under positive feedback is presented.
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