In this paper, asymmetric Algebraic Riccati Equations are analyzed. We derive a new parametrization of the set of solutions, which may be viewed as alternative to the classical one based on Lagrangian subspaces of a “pseudo-Hamiltonian” matrix. Generalizing the symmetric case, the proposed parametrization is given in terms of pairs of invariant subspaces of two related “feedback” matrices. Exte...

The Standard Model parametrization of CP violation is described. Tests of this parametrization using the observed heavy flavour decays and implications for New physics are discussed.

As a matter of fact, the solution space of many systems of ordinary differential (OD) or partial differential (PD) equations in engineering or mathematical physics ”can/cannot” be parametrized by a certain number of arbitrary functions behaving like ”potentials”. In view of the explicit examples to be met later on, it must be noticed that the parametrizing operator, though often of the first or...

This report addresses the problem of computing the parametrization of the intersection of deformable quadratic algebraic surfaces (quadrics) in projective space. It also presents an automatic method for describing the evolution in time of the topology of the intersection. The work is based on the results from [3, 4], which offer an exact parametrization of the intersection of two quadrics with ...

We determine necessary and sufficient conditions for a tubular surface to be swung, and viceversa. From these characterizations, we derive two symbolic algorithms. The first one decides whether a given implicit equation, of a tubular surface, admits a swung parametrization and, in the affirmative case, it outputs such a parametrization. The second one decides whether a given swung surface param...

This paper is concerned with the parametrization of nonlinear state feedback controllers via kernel representations. First we de ne an appropriate stability for state feedback systems. Second it is shown that the stability condition can be reduced to the internal stability of a speci c type of output feedback system. Finally the state feedback parametrization will be derived based on the existi...