Authors:
Keqin Gu,
Qing-Long Han,
Volume: 1, Page 2793 Paper number 47
Abstract:
This paper investigates the controller synthesis of uncertain linear
time-delay systems. Stabilizability criteria are derived based on a
discretized Lyapunov functional approach. A new controller design method
is developed. Numerical examples show that the results using the proposed
method are less conservative than some existing ones.
Authors:
Papa Momar Ndiaye,
Michel Sorine,
Volume: 1, Page 2799 Paper number 13
Abstract:
We study the variations of the quadratic performance associated to
a linear differential system of retarded type for small values of the
delays. From an interpretation of delays as singular perturbations
of abstract evolution operators, we revisit the usual theory of representation
and optimal control of retarded systems. This leads to a new parameterization
of associated Riccati operators for which insight is gained in the
dependence on the delays. This explicit parameterization of Riccati
operators by the delays enables us to prove differentiability at zero
for performance viewed as a function of the delays, in the LQ-optimal
or H-infinity sub-optimal control. The gradient is explicitly computed
in terms of the non-negative solution of the finite dimensional Riccati
equation associated to the non-delay control problem.
Authors:
Keqin Gu,
Volume: 1, Page 2805 Paper number 1674
Abstract:
An integral inequality is derived, and applied to the stability problem
of time-delay systems using discretized Lyapunov functional formulation.
As the result, a simpler stability criterion is derived.
Authors:
Silviu-Iulian Niculescu,
Chaouki T. Abdallah,
Volume: 1, Page 2811 Paper number 1485
Abstract:
This paper addresses conditions for characterizing static output feedback
controllers including delays for some proper (finite-dimensional) transfer
functions. The interest of such study is in controlling systems which
can not be stabilized by the classical, nondelayed static output feedback,
and its difficulty lies in computing delay intervals guaranteeing closed-loop
stability, since stability switches/reversals may occur for the same
(matrix) gain if the delay is seen as a 'free' (design) parameter.
The derived conditions are expressed in terms of some appropriate matrix
pencils or MIMO Nyquist tests. Illustrative examples are also presented.
Authors:
Giuseppe L. Conte,
Anna Maria Perdon,
Volume: 1, Page 2817 Paper number 2038
Abstract:
The notion of invertibility for systems with coefficients in a ring
is investigate. An algebraic notion of relative degree is introduced
and used to characterize the invertibility of a SISO system, while
a geometric characterization of relative degree is given for the MIMO
case. Application to the study of delay differential systems are presented.
Authors:
Vladimir Rasvan,
Silviu-Iulian Niculescu,
Rogelio Lozano,
Volume: 1, Page 2823 Paper number 8016
Abstract:
Multivariable linear systems with several delays are considered. Delays
are allowed in the state as well as in the input or the output. Passivity
and dissipativity of such systems are considered both in the input-output
and state space framework in connection with hyperstability. In the
input-output framework necessary and sufficient conditions of passivity
and hyperstability of delay systems are given in the language of positive
real functions. Furthermore, necessary and st@cient conditions for
positive realness are derived for a class of meromorphic functions
describing delay systems.
Authors:
Young Soo Suh,
Volume: 1, Page 2829 Paper number 9149
Abstract:
Analytic solution of Lyapunov functional equations of distributed delay
systems is derived. The analytic solution is computed using a matrix
exponential function, while conventional computation has been relied
on numerical approximations. Based on the analytic solution, a stability
condition for distributed delay systems with unknown but bounded constant
delay is proposed.
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