Search results for "Polynomial matrix"
showing 4 items of 4 documents
On complete set of solutions for polynomial matrix equations
1990
Abstract In this paper we introduce the concept of co-solution of a polynomial matrix equation which permits us to obtain necessary and sufficient conditions so that a set of solutions be a complete set.
Determinantal sets, singularities and application to optimal control in medical imagery
2016
International audience; Control theory has recently been involved in the field of nuclear magnetic resonance imagery. The goal is to control the magnetic field optimally in order to improve the contrast between two biological matters on the pictures. Geometric optimal control leads us here to analyze mero-morphic vector fields depending upon physical parameters , and having their singularities defined by a deter-minantal variety. The involved matrix has polynomial entries with respect to both the state variables and the parameters. Taking into account the physical constraints of the problem, one needs to classify, with respect to the parameters, the number of real singularities lying in som…
Response determination of linear dynamical systems with singular matrices: A polynomial matrix theory approach
2017
Abstract An approach is developed based on polynomial matrix theory for formulating the equations of motion and for determining the response of multi-degree-of-freedom (MDOF) linear dynamical systems with singular matrices and subject to linear constraints. This system modeling may appear for reasons such as utilizing redundant DOFs, and can be advantageous from a computational cost perspective, especially for complex (multi-body) systems. The herein developed approach can be construed as an alternative to the recently proposed methodology by Udwadia and coworkers, and has the significant advantage that it circumvents the use of pseudoinverses in determining the system response. In fact, ba…
New Results in Generalized Minimum Variance Control of Computer Networks
2014
In this paper new results in adaptive (generalized) minimum variance control of packet switching computer networks are presented. New solutions, corresponding to the new inverses of the nonsquare polynomial matrices, can be used for design of robust control of multivariable systems with different number of inputs and outputs. Application of polynomial matrix inverses with arbitrary degrees of freedom creates the possibilities to optimal control of computer networks in terms of usage their maximal bandwidth. Simulation examples made in Matlab environment show big potential of presented approach. DOI: http://dx.doi.org/10.5755/j01.itc.43.3.6268