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.
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.
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.
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.
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.
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.
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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