J.F. Lafay

Solution to Morgan's problem

A necessary and sufficient condition is presented for the solution of the row-by-row decoupling problem (known as Morgans problem) in the general case, that is, without any restrictive assumption added to the system to the feedback law u=Fx+Gy (G may be noninvertible). This is a structural condition in terms of invariant lists of integers which are easily computable from a given state realization of the system. These integers are the infinite zero orders (Morses list I/sub 4/) and the essential orders of the system, which only depend on the input-output behavior, and Morses list I/sub 2/ of the system, which depends on the choice of a particular state realization. >

Regular paper: Model matching for linear systems with delays and 2D systems

Model matching problem for linear systems with delays is considered, via a transfer matrix approach. We deal with a general class of neutral delay-differential systems, which is equivalent to 2D systems, from a realizability point of view. The solution of the problem is based on the decomposition of the ring of the causal rational functions (which is not a principal ideal domain) as the intersection of two suitable principal ideal domains.

On the structure at infinity of linear block-decouplable systems: The general case

The aim of this note is to show that a linear system ( C, A, B ) is block-decouplable by means of static state feedback laws ( F, G ) with G invertible if and only if the infinite structure of ( C, A, B ) equals the union of the infinite structures of the subsystems ( C_{i}, A, B ) extracted from the given output partition. This result generalizes the ones recently obtained for Morgans problem [6] and for the particular cases of right-invertible [7] or left-invertibie [8] systems.

Decoupling by restricted static-state feedback: The general case

In this paper we tackle the general block decoupling problem, for linear constant dynamical systems ( C, A, B ) with m inputs and p outputs, with restricted static-state feedback, in other words with control laws of type u = GFx + Gv . We give a necessary and sufficient condition of existence for such laws which generalizes the one previously given in [2] for the simple case k = p leq m , where k denotes the number of blocks to be decoupled.

The row-by-row decoupling via state feedback: a polynomial approach

Necessary and sufficient conditions for the row-by-row and integrator decoupling of a linear system x = Ax + Bu, y = Cx via nonregular static state feedback are established. A procedure is outlined to calculate one such gain.

Implementation of a distributed control law for a class of systems with delay

Abstract The use of distributed delays in the control law of time-delay systems has been proposed by several authors. The implementation of such controllers is not trivial, and recent publication shown that replacing the distributed delay operator by an approximation computed through pointwise delay operators was unsafe with respect to the stability of the systen1. In this paper the use of digital controller is addressed, for the control of systems with an input delay. Practically, this means replacing an integral by a recurrent system. The first approach was to use a method of numerical approximation of an integral to build the recurrence law. In this paper it is shown that a such controller, built with the Simpson method, leads to an unstable closed-loop system. A second approach leads to the construction of a control law which realizes a sampled pole assignment, in the same way as the distributed control law realizes a pole assignment in continuous time.

Model Matching for Linear Systems with Delays

Abstract Model Matching Problem for linear systems with delays is considered. The delays we consider are commensurate and we use a ring model. The problem is that the ring of the causal transfer functions is not principal, where causal means realizable. That is why we have to introduce two decompositions of the space, relatively to two different principal rings, whose intersection is the ring of the causal transfer functions. Then, we give necessary and sufficient conditions to the Model Matching Problem, in the general case.

A survey on Morgan's problem

We give for the first time a necessary and sufficient condition for the solution of the row by row decoupling problem by (non regular) static state feedback. This is a structural condition in terms of invariant lists of integers.

A Unified Study of the Fixed Modes of Systems Decoupled via Regular Static State Feedback

It is well known that one cannot always achieve simultaneously block decoupling and complete freedom of pole assignment. The modes that cannot be assigned are called the fixed modes of the decoupled system.Their interest is obvious : their value determines the ability of a system to be decoupled with stability or not.

Solution of the static-state feedback decoupling problem for linear systems with two outputs

We give for linear systems with two outputs a necessary and sufficient condition for the solvability of the restricted decoupling problem (RDP) in terms of some structural invariants. A geometric characterization is also given which provides the least dynamical extension needed when RDP is not solvable.