Authors:
Chung-Yao Kao,
Muralidhar Ravuri,
Alexander Megretski,
Volume: 1, Page 1477 Paper number 1981
Abstract:
In this paper, we consider the control synthesis problem when the disturbance
input w is within a set defined by several dynamic Integral Quadratic
Constraints (IQCs). We show that the condition on the existence of
a stabilizing controller can be expressed as a set of Linear Matrix
Inequalities (LMIs). We also show that the stabilizing controllers,
if exist, have the dimension no larger than the sum of the dimension
of the open-loop system and the multipliers in IQCs.
Authors:
Didier Henrion,
Gjerrit Meinsma,
Volume: 1, Page 1483 Paper number 1633
Abstract:
We describe a new proof of the well-known Lyapunov's matrix inequality
about the location of the eigenvalues of a matrix in some region of
the complex plane. The proof makes use of standard facts from quadratic
and semi-definite programming. Links are established between the Lyapunov
matrix, rank-one LMIs and the Lagrange multiplier arising in duality
theory.
Authors:
Pierre Apkarian,
Hoang Duong Tuan,
Jacques Bernussou,
Volume: 1, Page 1489 Paper number 1846
Abstract:
The paper describes a new framework for the analysis and synthesis
of control systems, which constitutes a genuine continuous-time extension
of results that are only available in discrete-time. In Contrast to
earlier results the proposed methods involve a specific transformation
on the Lyapunov variables and a reciprocal variant of the Projection
Lemma, in addition to the classical linearizing transformations on
the controller data. For a wide range of problems including robust
analysis and synthesis, multi-chanel H2 state and output-feedback syntheses,
the approach leads to potentially less conservative LMI characterizations.
This comes from the fact that the technical restriction of using a
single Lyapunov function is to some extent ruled out in this new approach.
Moreover, the approach offers new potentials for problems that cannot
be handled using earlier techniques. As an instance, the eigenstructure
assignment problem blended with Lyapunov-type constraints is given
a simple and tractable formulation.
Authors:
Anas Fattouh,
Olivier Sename,
Jean-Michel Dion,
Volume: 1, Page 1495 Paper number 1481
Abstract:
This paper is concerned with a robust observer design for linear time-delay
systems via linear matrix inequality approach. The proposed method
not only guarantees the stability of the proposed observer, but also
reduces the effects of different unstructured uncertainties (like the
additive uncertainty, the input multiplicative uncertainty,...) on
the estimated error.
Authors:
Graziano Chesi,
Andrea Garulli,
Alberto Tesi,
Antonio Vicino,
Volume: 1, Page 1501 Paper number 1868
Abstract:
This paper considers the problem of solving certain classes of polynomial
systems. This is a well known problem in control system analysis and
design. A novel approach is developed as a possible alternative to
the commonly employed algebraic geometry and homotopy methods. The
first result of the paper shows that the solution set of the polynomial
system belongs to the kernel of a symmetric matrix. Such a matrix is
obtained via the solution of a suitable Linear Matrix Inequality (LMI)
involving the maximization of the minimum eigenvalue of an affine family
of symmetric matrices. The second result concerns the computation of
the solutions from the kernel of the obtained matrix. In particular,
it is shown that the solutions can be recovered quite easily if the
dimension of the kernel is smaller than the degree of the polynomial
system. Finally, some application examples are illustrated to show
the features of the approach and to make a brief comparison with the
algebraic geometry techniques.
Authors:
Te-Jen Su,
Chien-Yu Lu,
Gw-Jia Jong,
Volume: 1, Page 1507 Paper number 8003
Abstract:
This paper provides new stability criteria for a class of uncertain
linear time-delay systems with time-varying delays. Based on Lyapunov-Krasovskii
functionals combining with LMI techniques, improved delay-dependent
robust stability criteria, which are given in terms of quadratic forms
of state and LMI, are derived. Our results shown by an example are
less conservative than the existing stability criteria.
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