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On the computation of a reduced set of quadratic Plucker relations and their use in the solution of the determinantal assignment problem.

Kalogeropoulos G., Kytagias D.

Systems Science

2000

Vol. 26, nr 2

5-25

An algorithmic method is presented for the computation of a reduced set of quadratic Plucker relations describing completely the Grassmann variety of the corresponding projective space. In particular, it is proven that a set of three terms homogeneous equations can be extracted from the whole set of quadratic Plucker relations. This set contains a specific number of equations, which exactly-constitute a reduced set of quadratic Plucker relations. This is achieved by using a simple criterion based on a correspondence between the coordinates of a decomposable vector and lexicographical orderings. In addition, the algorithm suggested is error-free from numerical computations. The above theory is used for the development of a unifying approach for pole assignment by state and output feedback, for asymptotic observer design and for zero assignment by squaring down for linear time-invariant regular type control systems.

Model reference adaptive controller design for mimo linear systems based on multirate generalized sampled-data hold functions.

Arvantis K.G., Sigrimis N., Kookos I.K., Kalogeropoulos G.

Systems Science

1999

Vol. 25, nr 3

5-36

The use of multirate generalized sampled-data hold functions for model reference adaptive control of linear multiple-input, multiple-output (MIMO) systems with unknown parameters, is investigated in this paper , for the firs time. Such a control scheme contains a multirate sampling mechanism with different sampling period to each system input and relies on two periodically varying modulating matrix functions. The proposed control strategy allows us to assign an arbitrary discrete-time transfer function matrix for the sampled close-loop system and does not make assumptions on the plant other than controllability and observability of the continuous and the sampled system, and the knowledge of a set of structural indices, namely the locally minimum controllability indices of the continuous-time plant. The indirect adaptive control scheme presented here, estimates the unknown plant parameters (and hence the parameters of the desired modulating matrix functions) on line, from sequential data of the inputs and the outputs of the plant, which are recursively updated within the time limit imposed by a fundamental sampling period T0. The controller determination is reduced to the simple problem of solving a linear algebraic system of equation, whereas known indirect model reference adaptive control techniques require the solution of matrix polynomial Diophantine equations, whose solution may become unstable. Moreover, persistency of excitation and, therefore, parameter convergence, of the continuous-time plant is provided without making assumptions either on the existence of specific convex sets in which the estimated parameters belong or on the coprimeness of the polynomials describing the ARMA model, or finally on the richness of the reference signals, as compared to known indirect model reference adaptive control schemes.