Authors:
Ling Hou,
Anthony N. Michel,
Volume: 1, Page 3854 Paper number 1057
Abstract:
We present new Lyapunov and Lagrange stability results for pulse-width-modulated
(PWM) feedback systems with linear plants. We consider the non-critical
case, where the poles of the transfer function of the plant are all
in the left-half of the complex plane and the critical case, where
one pole is at the origin while the remaining poles are all in the
left-half of the complex plane. For these systems we apply the Direct
Method of Lyapunov to establish new and improved stability results.
As in most existing results for PWM feedback systems obtained by the
Lyapunov method, we employ quadratic Lyapunov functions in our analysis.
However, in the proofs we make use of different majorizations, requiring
hypotheses that differ significantly from those used in the existing
results. Additionally, and perhaps more importantly, we incorporate
into our results optimization procedures that improve our results significantly.
We demonstrate the applicability and quality of our results by means
of two specific examples that are identical to examples presented in
the literature.
Authors:
Bernd Tibken,
Volume: 1, Page 3860 Paper number 1853
Abstract:
Investigation of the stability properties of stationary points of nonlinear
systems lies at the heart of modern control engineering. In this contribution
we will show how modern results of real algebraic geometry, a branch
of pure mathematics, will be used to compute subsets of the region
of attraction of asymptotically stable stationary points of polynomial
systems. This computation will be done in a numerically stable and
efficient way by reformulating the problem as a linear matrix inequality
(LMI). For this reformulation new results from real algebraic geometry
will be used. The results presented in this contribution show very
clearly that a multidisciplinary approach to nonlinear control systems
leads to new insight and new powerful conditions. Some conclusions
and an outlook will finish this contribution.
Authors:
Alexander Yu. Pogromsky,
Henk Nijmeijer,
Volume: 1, Page 3865 Paper number 9606
Abstract:
Conditions are given that guarantee the convergence of arbitrary solutions
of an autonomous dynamical system towards some equilibrium point of
the system. The conditions are formulated in terms of matrix inequalities
involving the variational equation. A connection with analytic estimates
of the Hausdorff dimension of invariant compact sets is given.
Authors:
Bernd Tibken,
Ossama Hachicho,
Volume: 1, Page 3870 Paper number 1854
Abstract:
Investigation of the stability properties of stationary points of nonlinear
systems lies at the heart of modern control engineering. In this contribution
we will show how the theorem of Ehlich and Zeller is used to compute
subsets of the domain of attraction of asymptotically stable stationary
points of polynomial systems. The theorem of Ehlich and Zeller is a
tool to bound the values of a polynomial over an interval using the
values of the polynomial on a finite grid in the interval. We will
present the generalizations of this theorem to multivariable polynomials
and to trigonometric polynomials. A bisection strategy will be presented
which allows the guaranteed computation of a subset of the domain of
attraction. An instructive example will be presented and some conclusions
and an outlook will finish this contribution.
Authors:
Frédéric Mazenc,
Laurent Praly,
Volume: 1, Page 3875 Paper number 1129
Abstract:
For nonaffine nonlinear feedforward systems classes of control Lyapunov
functions are constructed. Explicit formulas are determined in an important
particular case. As an application of this design, we prove that the
bounded state feedbacks constructed induce the property of nonlinear
disturbance-to-state L^p stability.
Authors:
Driss Boutat,
Mohamed Djemai,
Jean-Pierre Barbot,
Volume: 1, Page 3881 Paper number 1438
Abstract:
This paper deals with the decomposition of the drift term of nonlinear
multivariable regular systems. A transverse and tangent decomposition
of the vector field is presented, then a feedback neutralizing the
transverse part is studied. Zero dynamics stability is considered and
sufficient conditions to obtain a global passivity of the system are
given. An other decomposition based on the workless field; attracting
field; and rejecting field is also studied. Some illustrative example
s are given all along the paper. Key Words: Structural analysis, Control
Design, Stability, Passivity, Nonlinear multivariable systems.
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