Authors:
Izumi Masubuchi,
Volume: 1, Page 3636 Paper number 127
Abstract:
This paper is concerned with stability and stabilization of implicit
systems. Stability criteria are provided in terms of the Kronecker
form, Lyapunov equation and inequality and conditions on extended rank
and invertibility of the system pencil. Then stabilization of implicit
systems via interconnection is considered based on the notion of initial-freedom
preservation as a formulation of regularity of interconnection. To
analyze stabilization with initial-freedom preservation, we define
complete-stabilizability and zero-detectability. It is shown that stabilizability
via interconnection with initial-freedom preservation is equivalent
to complete-stabilizability and zero-detectability. Thus standard results
on output feedback stabilization of state-space and descriptor systems
are generalized to stabilization of implicit systems via interconnection.
Authors:
Moisés Bonilla-Estrada,
Michel Malabre,
Volume: 1, Page 3642 Paper number 1323
Abstract:
We extend here some of our previous results on non square implicit
descriptions which can be used for modelling broader classes of linear
systems, for instance systems with internal switches. We introduce
ladder systems, for which, though the input-output behaviour can vary
from a first order to nth order system (depending on the position of
the internal switches), the non square (flat) implicit description
is unique. When some conditions are satisfied (on the basis some of
our previous results), it is possible to control such an implicit system
so that it behaves as a pre-specified model. Our presentation here
is mainly oriented towards modelling, with a particular example extracted
from agronomical applications.
Authors:
Hiroaki Mukaidani,
Hua Xu,
Koichi Mizukami,
Volume: 1, Page 3648 Paper number 8021
Abstract:
In this paper, we study the linear quadratic Nash games for infinite
horizon singularly perturbed systems. In order to solve the problem,
we must solve a pair of cross-coupled algebraic Riccati equations with
a small positive parameter. As a matter of fact, we propose a new algorithm,
which combines Lyapunov iterations and the generalized Lyapunov equation
direct method, to solve the cross-coupled algebraic Riccati equations.
The new algorithm ensures that the solution of the cross-coupled algebraic
Riccati equations converges to a positive semidefinite stabilizing
solution. Furthermore, in order to solve the cross-coupled algebraic
Riccati equations, we propose a new Riccati iterations method different
from existing method. As another important feature of this paper, our
method is applicable to both standard and nonstandard singularly perturbed
systems.
Authors:
Vasile Dragan,
Toader Morozan,
Peng Shi,
Volume: 1, Page 3654 Paper number 1582
Abstract:
In this paper, we study the problem of asymptotic property of the norm
of input-output operators related to a class of singularly perturbed
stochastic linear systems. The system is under perturbation of multiplicative
white noise. By using reduction order and boundary layer techniques,
it is shown that the norm of the operator of the perturbed system is
less than a given number (gamma) when the small perturbation (varepsilon)
tends to zero, if both the related norms of the reduced subsystem
and the boundary layer subsystem are less than (gamma).
Authors:
G.R. Duan,
G.P. Liu,
S. Thompson,
Volume: 1, Page 3660 Paper number 1724
Abstract:
Based on a recently proposed complete parametric approach for eigenstructure
assignment in descriptor linear systems via output feedback, disturbance
decoupling using output feedback in descriptor linear systems is investigated.
Both the dynamical and static disturbance decoupling problems are
tackled. Necessary and sufficient conditions for both problems are
proposed in terms of the closed-loop eigenvalues and eigenvectors.
By arranging these conditions into constraints on the design parameters
provided by eigenstructure assignment, the disturbance decoupling problems
are converted into eigenstructure assignment problems with extra parameter
constraints. The approach guarantees closed-loop regularity, offers
certain flexibility and can provide all the degrees of design freedom.
An example is investigated to show the effect of the proposed approach.
Authors:
Li Lee,
Jian Liung Chen,
Volume: 1, Page 3666 Paper number 1435
Abstract:
In this paper, the strictly positive real (SPR) lemma for discrete-time
descriptor systems is addressed. The relationship between strict positive
realness and bounded realness (BR) of transfer matrices for such systems
is developed. Based on this development, an LMI-based necessary and
sufficient condition for a descriptor system being admissible and simultaneously
SPR is established.
Authors:
Tadeusz Kaczorek,
Volume: 1, Page 3668 Paper number 1010
Abstract:
The concepts of anticipatory discrete-time and continuous-time systems
for singular linear systems are introduced. Necessary and sufficient
conditions for anticipation of the linear systems are established.
It is shown that the anticipation of singular systems is not invariant
under state-feedbacks. A procedure is presented for a suitable choice
of state feedback for anticipatory (not anticipatory) system such that
the closed loop system is not anticipatory (is anticipatory).
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