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Parametrization and geometric analysis of coordination controllers for multi-agent systems

Xiaoli Wang, Yiguang Hong (2009)

Kybernetika

In this paper, we address distributed control structures for multi-agent systems with linear controlled agent dynamics. We consider the parametrization and related geometric structures of the coordination controllers for multi-agent systems with fixed topologies. Necessary and sufficient conditions to characterize stabilizing consensus controllers are obtained. Then we consider the consensus for the multi-agent systems with switching interaction topologies based on control parametrization.

Poles and zeroes of nonlinear control systems

Jean-François Pommaret (2002)

Kybernetika

During the last ten years, the concepts of “poles” and “zeros” for linear control systems have been revisited by using modern commutative algebra and module theory as a powerful substitute for the theory of polynomial matrices. Very recently, these concepts have been extended to multidimensional linear control systems with constant coefficients. Our purpose is to use the methods of “algebraic analysis” in order to extend these concepts to the variable coefficients case and, as a byproduct, to the...

Polynomial systems theory applied to the analysis and design of multidimensional systems

Jari Hatonen, Raimo Ylinen (2003)

International Journal of Applied Mathematics and Computer Science

The use of a principal ideal domain structure for the analysis and design of multidimensional systems is discussed. As a first step it is shown that a lattice structure can be introduced for IO-relations generated by polynomial matrices in a signal space X (an Abelian group). It is assumed that the matrices take values in a polynomial ring F[p] where F is a field such that F[p] is a commutative subring of the ring of endomorphisms of X. After that it is analysed when a given F[p] acting on X can...

Predictability and control synthesis

Philippe Declerck (1999)

Kybernetika

Processes modeled by a timed event graph may be represented by a linear model in dioïd algebra. The aim of this paper is to make temporal control synthesis when state vector is unknown. This information loss is compensated by the use of a simple model, the “ARMA” equations, which enables to introduce the concept of predictability. The comparison of the predictable output trajectory with the desired output determines the reachability of the objective.

Proper feedback compensators for a strictly proper plant by polynomial equations

Frank Callier, Ferdinand Kraffer (2005)

International Journal of Applied Mathematics and Computer Science

We review the polynomial matrix compensator equation X_lD_r + Y_lN_r = Dk (COMP), e.g. (Callier and Desoer, 1982, Kučera, 1979; 1991), where (a) the right-coprime polynomial matrix pair (N_r, D_r) is given by the strictly proper rational plant right matrix-fraction P = N_rD_r, (b) Dk is a given nonsingular stable closed-loop characteristic polynomial matrix, and (c) (X_l, Y_l) is a polynomial matrix solution pair resulting possibly in a (stabilizing) rational compensator given by the left fraction...

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