Nonlinear Time Varying Systems

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Author Index
A B C D E F G H I
J K L M N O P Q R
S T U V W X Y Z

UGAS Of Nonlinear Time-Varying Systems: A Delta-Persistency Of Excitation Approach

Authors:

Antonio Loría, Elena Panteley, Andrew R. Teel,

Volume: 1, Page 3489 Paper number 1314

Abstract:

We study the problem of stability analysis for certain nonlinear systems. Our contributions are new tools to guarantee uniform global asymptotic stability (UGAS) of nonlinear time-varying (NLTV) systems. Firstly, we provide new definitions of persistency of excitation (PE). In particular, we give here a new definition of uniform delta-PE which, though conceptually equivalent to the original one introduced earlier by the authors, in the ECC '99, is mathematically less conservative. We also provide with some properties of delta-PE pairs (functions) and contribute with a result which establishes UGAS of NLTV systems under uniform delta-PE.

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New Stability Results for Time-Varying Systems Based on a Modified Detectability Condition

Authors:

Ti-Chung Lee, Ching-Hung Lee,

Volume: 1, Page 3495 Paper number 1764

Abstract:

The uniformly asymptotical stability is investigated from the output-to-state viewpoint for general nonlinear time-varying systems. Several criterions are proposed using some integral inequalities involving the output function and a new detectability condition. Furthermore, the existing results using the Lyapunov direct method such as the Krasovskii-LaSalle invariance principle, a theorem of Aeyels and a theorem of Khalil for time-varying systems are shown to be deduced for the proposed scheme. From these applications, it can be seen that as the invariance principle of LaSalle is used in studying the stability of time-invariant systems, our results can be also used in studying the stability of time-varying systems.

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On Input-to-State Stability for Time Varying Nonlinear Systems

Authors:

Heather A. Edwards, Yuandan Lin, Yuan Wang,

Volume: 1, Page 3501 Paper number 1983

Abstract:

Input-to-state stability (ISS, for short) was introduced in the late 1980's by E.D. Sontag. This property naturally incorporates an important concept ``finite gain'' frequently used in engineering with the classic stability notation used in ordinary differential equations, replacing the linear gain functions for general nonlinear systems by nonlinear gain functions. However, most theoretical developments dealt mainly with time invariant systems. On the other hand, it is very often the case that the systems under consideration are time varying. Such a situation often arises from, e.g., trajectory tracking problems. It is thus natural to understand the ISS property for time varying systems. In this work, we focus on the Lyapunov characterizations of input-to-state stability for time varying nonlinear systems, and in particular, for periodic time varying systems. We show that a periodic time varying system is ISS if and only if it admits an ISS-Lyapunov function V(t, x) that is also periodic in the variable t. A small gain theorem for time varying nonlinear systems is also presented in this work.

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On the Existence of Common Lyapunov Triples for ISS and iISS Switched Systems

Authors:

José Luis Mancilla Aguilar, Rafael Antonio García,

Volume: 1, Page 3507 Paper number 1300

Abstract:

In this paper we present converse Lyapunov theorems for input-to-state stable (ISS) and integral-input-to-state stable (iISS) switched nonlinear systems. Their proofs are based on existing converse Lyapunov theorems for input-output-to-state stable (IOSS) and iISS nonlinear systems, and on the association of the switched system with a nonlinear system with inputs and disturbances that take values in a compact set.

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A Unified Characterization And Solution Of Input-To-State Stabilization Via State-Dependent Scaling

Authors:

Hiroshi Ito,

Volume: 1, Page 3513 Paper number 1431

Abstract:

The paper shows new solutions to input-to-state stabilization and integral input-to-state stabilization problems for nonlinear systems based on the novel concept of state-dependent scaling design. Both state-feedback and output-feedback controllers are constructed in a unified way. The method provides global solutions whenever the system is in the strict-feedback or output-feedback form. The paper encompasses input-to-state stabilization and integral input-to-state stabilization in the presence of structured, static and dynamic uncertainties.

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New State-Dependent Scaling for Uncertain Dynamics: Nonlinear Global Stabilization and Performance

Authors:

Hiroshi Ito,

Volume: 1, Page 3519 Paper number 1376

Abstract:

This paper proposes a simple and systematic design approach to global robust stabilization of nonlinear systems in the presence of dynamic and static uncertainties. An extended concept of state-dependent scaling is newly introduced for robustification of feedback control against dynamic uncertainties. This paper presents a recursive design procedure which provides a global stabilizing state-feedback controller whenever the system belongs to a new class of strict-feedback systems allowing both dynamic and static uncertainties. The state-dependent scaling method reduces problems of robust L_2 disturbance attenuation and robust almost disturbance decoupling to a special case of the robust stabilization design.

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On Formulating Nonlinear Dynamics in LPV Form

Authors:

Douglas J. Leith, William E. Leithead,

Volume: 1, Page 3526 Paper number 1659

Abstract:

The shortcomings of a popular LPV gain-scheduling design approach are demonstrated by a simple counter-example. It is shown that, for a very general class of nonlinear systems, such an ad hoc design approach is unnecessary since soundly-based methods exist for transforming the plant dynamics into LPV/quasi-LPV form.

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