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Results obtained previously for controlled invariant subspaces for systems over rings are generalized to stabilizability subspaces. Stability is defined based on an axiomatically introduced concept of convergence. The results are applied to the problem of disturbance decoupling with internal stability for systems over rings.
The problems of determining the minimal order of a stabilizing compensator for a fixed linear, multivariable system and for the generic p × m system of fixed degree are considered. An elementary geometric argument gives sufficient conditions for the generic stabilizability by a compensator of order ≤ q. A more delicate geometric argument, involving pole-placement in the high gain limit, is then used...
Resume Dans cet article, le problème du découplage par blocs des systèmes linéaires multivariables est étudié. Il est montré que la structure à l'infini de la matrice de transfert du système joue un rôle prépondérant. Dans le cas des systèmes inversibles à gauche (systèmes injectifs), on donne une condition nécessaire et suffisante de découplage par retour d'état statique. Cette condition, qui s'exprime...
Resume La structure à l'infini des systèmes linéaires invariants (nombre de zéros infinis et leur multiplicité) a été l'objet de nombreux travaux récents. Dans le cas des triplets invariants, COMMAULT et DION [10] ont été les premiers à en proposer une caractérisation géométrique. En utilisant la même approche, nous proposons dans la première partie une interprétation des multiplicités des zéros infinis...
Ways are discussed of using singular-value decompositions of operator-valued functions of the complex frequency variable in the analysis and design of linear multivariable feedback systems. The local and global behaviour of such a decomposition is briefly discussed. Ways in which phase information may be added to singular values are considered, and the use of a particular method — the Quasi-Nyquist...
The problem of matching the performance of a given two-dimensional system to that of a desired model is considered. An algorithm is proposed which yields a static output feedback controller which, when applied to the open-loop system, results in a closed-loop system whose transfer function matrix matches approximately the transfer function matrix of the desired model. The approximation may be either...
This paper is concerned with the approximation of unstable input-output plants and their feedback interconnections. Systems are represented by closed operators with restricted domains in a Hilbert space. A metric on systems is introduced in terms of the gap (or aperture) between their graphs. It is shown that under the gap metric the mapping from the open to the closed loop system is...
Résumé Le comportement entrée/sortie de tout système non linéaire discret est caractérisé par une série qui s'exprime en termes d'opérateurs différentiels déduits de l'équation du système. A partir de cette série, on montre qu'un système non linéaire discret est subordonné à un système à état-affine si, et seulement si, un certain espace fonctionnel est de dimension finie.
Résumé On montre, par usage conjoint de l'algèbre différentielle et des séries génératrices non commutatives, que la sortie d'un système régulier (ou bilinéaire) satisfait une équation différentielle linéaire, dont les coefficients dépendent des entrées et de leurs dérivées.
The solidification of an alloy with N components is studied. The problem is modelized by a system of N nonlinear partial differential equations (the unknowns are the temperature and the concentrations). The temperature along the free-boundary (the interface solid-liquid) is unknown and depends on the concentrations. Following the idea of A. Crowley — J. Ockendon [7], G.J Fix [10] for a binary...
Automation principle, tested and applied on SACILOR mill furnaces The process described here takes into account the following1 -The real time-rate of the furnace métal-discharge, which is the variable of the response-curve for variable rate.2 -The transfer functions that are proper to the furnace are experimentally assesed. According to the applications, we take into account variable elements such...
The strong finite stochastic realization problem is given a probability space and a finite valued stochastic process, to show existence of and to classify all strong stochastic realizations of the given process that have a finite state space. In this paper the static version of this problem is investigated. Results are given on the classification of finite σ-algebra's that make two given finite σ-algebra's...
Using the measure-transformation approach, an exact, computable optimal filter for a particular class of nonlinear filtering problems in discrete time is derived. This filter is also used to approximate the optimal filter for a large class of discrete-time filtering problems arising in applications. Convergence of the approximations is proved and bounds on the quality of the approximations derived.
The continuous-time RM and KW procedures are modified to suit the case when the measurement error is the process of dependent increment. By using a combined method connecting the probabilistic method with the ordinary differential equation (ODE) method simple conditions are given to guarantee the convergence of algorithms to the zero and the extremum of regression functions.
This paper is concerned with an optimal stopping problem for a two-parameter stochastic process : the bi-Brownian motion on the unit bi-disc. It is shown that the Snell envelop of the cost function is itself a functional of the bi-Brownian motion, and it verifies a system of variational inequations similar to those of the classical theory. In the first part various notions of bi-potential theory are...
The problem of production management for an automated manufacturing system is described. The system consists of machines that can perform a variety of tasks on a family of parts. The machines are unreliable, and the main difficulty the control system faces is to meet production requirements while machines fail and are repaired at random times. A multi-level hierarchical control algorithm is proposed...
The application of system analysis to plastics injection moulding process is discussed. In contrast to well-known methods of white box modelling, which use insight into the physical phenomena of the process, the experimental approach of black box modelling is considered. This way of system analysis is intended to yield mathematical process models describing the static and dynamic relations of system...
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