Authors:
Ventsi G. Rumchev,
Volume: 1, Page 3159 Paper number 1075
Abstract:
Positive systems are defined as systems in which the state trajectory
is always positive (or at least non-negative) whenever the initial
state is positive (non-negative). Positive linear systems are defined
on cones and not on linear spaces and that is why the reachability
and controllability tests for linear systems prove to be false. In
this paper necessary and sufficient condition for reachability of discrete-time
positive linear systems with scalar input is proved. Criteria for recognizing
the reachability property of such systems are presented and complete
characterizations of the generic structure of reachable non-negative
pair (A, b) in both algebraic and graph-theoretic forms are developed.
The paper gives a new general treatment of reachability properties
of scalar-input positive linear systems.
Authors:
Carlos E.T. Dórea,
Jean-Claude Hennet,
Volume: 1, Page 3163 Paper number 1194
Abstract:
This work extends the concept of self-bounded (A,B)-invariant subspaces
to convex polyhedral sets. Self-bounded (A,B)-invariant polyhedra are
defined and characterized. Necessary and sufficient conditions under
which a given polyhedron is self-bounded are established in the form
of linear matrix relations. It is then shown that the class of self-bounded
sets contained in a given region has an infimum, that is, a self-bounded
set which is contained in any set of this class. The infimal set is
characterized and a numerical method is proposed for its computation
in the polyhedral case. It is also shown how these results can be extended
to systems subject to control constraints and bounded additive disturbances.
A numerical illustrative example is finally presented.
Authors:
Osamu Kaneko,
Takao Fujii,
Volume: 1, Page 3169 Paper number 1340
Abstract:
In this paper, we study discrete time dissipativeness. Particularly,
we focus on storage functions. Differently from the continuous time
case, every storage function is not necessarily a state function in
discrete time. For this problem, this paper shows that a every nonnegative
storage function is a state function in discrete time. In addition,
we provide some of the necessary and sufficient conditions for the
existence of the nonnegative storage function.
Authors:
Maria Elena Valcher,
Volume: 1, Page 3175 Paper number 1207
Abstract:
Nonnegative linear systems, which have been traditionally investigated
within the state-space framework, are here introduced and analyzed
by means of the behavioral approach. Starting from certain definitions
and results which have been presented in a recent paper by Nieuwenhuis
(Nieuwenhuis, J.W.. "When to call a linear system nonnegative". Linear
Algebraamp; its Appl., vol. 281, pp.43-58, 1998), we have explored
the general autonomous case, by deriving an extended set of necessary
and sufficient conditions for an autonomous behavior to be nonnegative.
Authors:
Laura Menini,
Antonio Tornambè,
Volume: 1, Page 3181 Paper number 1025
Abstract:
The problem of regulating the position of a simple mechanical system
subject to non-smooth impacts in finite time is considered. A simple
solution based on a discrete-time formulation of the problem is given
for the nominal system. After studying the problems arising with such
a compensator if a perturbation in the position of the constraint is
not taken into account, a different control law is proposed in order
to overcome such difficulties.
Authors:
Mohamed Boutayeb,
Mohamed Darouach,
Volume: 1, Page 3183 Paper number 124
Abstract:
In this note we give some results on the convergence of the Kalman
Filter (K.F.) when used as an observer for linear time-varying systems.
Based on the block-input / block-output state model, we prove that
the state observer given in [7] is equivalent to the K.F. algorithm.
One of the main features, however, is that no assumption on the invertibility
of the state matrix, namely Ak in the paper, is needed and the computational
requirements are reduced. Furthermore, the obtained result can be extended,
by duality, to resolve the state feedback control problem.
Authors:
Pierre-Olivier Malaterre,
Mustafa Khammash,
Volume: 1, Page 3188 Paper number 2005
Abstract:
The aim of this work is to present an application of recent methods
for solving the l1 design problem, based on the Scaled-Q approach,
on a high-order, non-minimum phase system. We start by describing the
system which is an open-channel hydraulic system (e.g.: an irrigation
canal). From the linearization and discretization of the set of two
partial-derivative equations, a state-space model of the system is
generated. This model is a high-order MIMO system (five external perturbations
w, five control inputs u, five controlled outputs z', five measured
outputs y, 65 states x) and is non-minimum phase. A controller is then
designed by minimizing the l1 norm of the impulse response of the transfer
matrix between the perturbation w and the output z=[z'; z''], where
the five additional variable z'' are defined as z''=D_u.u. Considering
this additional transfer (w to z'') in the minimization problem leads
to a better posed problem and provides much better robustness margins.
Time-domain template constraints are added in order to force integrators
into the controller. The numerical resolution of the problem proved
to be efficient, despite of the characteristics of the system. The
obtained results are compared in the time-domain to classical PID and
LQG controllers, both on linear and non-linear simulated plants. The
results proved to be very good in terms of performance and robustness,
in particular for the rejection of the worst-case perturbation.
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