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The purpose of this paper is to derive constructive necessary and sufficient conditions for the problem of disturbance decoupling with algebraic output feedback. Necessary and sufficient conditions have also been derived for the same problem with internal stability. The same conditions have also been expressed by the use of invariant zeros. The main tool used is the dual- lattice structures introduced by Basile and Marro [R4].
The purpose of this paper is to show that the method of controlled lagrangians and its hamiltonian counterpart (based on the notion of passivity) are equivalent under rather general hypotheses. We study the particular case of simple mechanical control systems (where the underlying lagrangian is kinetic minus potential energy) subject to controls and external forces in some detail. The equivalence makes use of almost Poisson structures (Poisson brackets that may fail to satisfy the Jacobi identity)...
The purpose of this paper is to show that the method of controlled
Lagrangians and its Hamiltonian counterpart (based on the notion
of passivity) are equivalent under rather general hypotheses. We
study the particular case of simple mechanical control systems
(where the underlying Lagrangian is kinetic minus potential
energy) subject to controls and external forces in some detail.
The equivalence makes use of almost Poisson structures (Poisson
brackets that may fail to satisfy the Jacobi identity)...
The energy in a square membrane Ω subject to constant viscous damping
on a subset decays exponentially in time
as soon as ω
satisfies a geometrical condition known as the “Bardos-Lebeau-Rauch” condition. The rate
of this decay satisfies
(see Lebeau [Math.
Phys. Stud.19 (1996) 73–109]). Here denotes the spectral abscissa of the
damped wave equation operator and is a number called
the geometrical quantity of ω and defined as follows.
A ray in Ω is the trajectory generated by the
free motion...
Universal tracking control is investigated in the context of a class of -input, -output dynamical systems modelled by functional differential equations. The class encompasses a wide variety of nonlinear and infinite-dimensional systems and contains – as a prototype subclass – all finite-dimensional linear single-input single-output minimum-phase systems with positive high-frequency gain. The control objective is to ensure that, for an arbitrary -valued reference signal of class (absolutely...
Universal tracking control is investigated in the context of a
class S of M-input, M-output dynamical systems modelled by
functional differential equations. The class
encompasses a wide variety of nonlinear and infinite-dimensional
systems and contains – as a prototype subclass – all
finite-dimensional linear single-input single-output minimum-phase
systems with positive high-frequency gain. The control objective
is to ensure that, for an arbitrary -valued reference signal
r of class W1,∞ (absolutely...
The reference trajectory tracking problem is considered in this paper and (constructive) sufficient conditions are given for the existence of a causal state feedback solution. The main result is introduced as a byproduct of input-output feedback linearization.
Equivalence of several feedback and/or feedforward compensation schemes in linear systems is investigated. The classes of compensators that are realizable using static or dynamic, state or output feedback are characterized. Stability of the compensated system is studied. Applications to model matching are included.
We show how we can transform the and control problems of descriptor systems with invariant zeros on the extended imaginary into problems with state-space systems without such zeros. Then we present necessary and sufficient conditions for existence of solutions of the original problems. Numerical algorithm for control is given, based on the Nevanlinna-Pick theorem. Also, we present an explicit formula for the optimal controller.
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