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Infinite elementary divisor structure-preserving transformations for polynomial matrices

Nicholas Karampetakis, Stavros Vologiannidis (2003)

International Journal of Applied Mathematics and Computer Science

The main purpose of this work is to propose new notions of equivalence between polynomial matrices that preserve both the finite and infinite elementary divisor structures. The approach we use is twofold: (a) the 'homogeneous polynomial matrix approach', where in place of the polynomial matrices we study their homogeneous polynomial matrix forms and use 2-D equivalence transformations in order to preserve their elementary divisor structure, and (b) the 'polynomial matrix approach', where some conditions...

Input-output decoupling of nonlinear recursive systems

Ülle Kotta (2000)

Kybernetika

The input-output decoupling problem is studied for a class of recursive nonlinear systems (RNSs), i. e. for systems, modelled by higher order nonlinear difference equations, relating the input, the output and a finite number of their time shifts. The solution of the problem via regular static feedback known for discrete-time nonlinear systems in state space form, is extended to RNSs. Necessary and sufficient conditions for local solvability of the problem are proposed. This is the alternative to...

Invariant factors assignment for a class of time-delay systems

Jean-Jacques Loiseau (2001)

Kybernetika

It is well–known that every system with commensurable delays can be assigned a finite spectrum by feedback, provided that it is spectrally controllable. In general, the feedback involves distributed delays, and it is defined in terms of a Volterra equation. In the case of multivariable time–delay systems, one would be interested in assigning not only the location of the poles of the closed–loop system, but also their multiplicities, or, equivalently, the invariant factors of the closed–loop system....

Invariant measures and controllability of finite systems on compact manifolds

Philippe Jouan (2012)

ESAIM: Control, Optimisation and Calculus of Variations

A control system is said to be finite if the Lie algebra generated by its vector fields is finite dimensional. Sufficient conditions for such a system on a compact manifold to be controllable are stated in terms of its Lie algebra. The proofs make use of the equivalence theorem of [Ph. Jouan, ESAIM: COCV 16 (2010) 956–973]. and of the existence of an invariant measure on certain compact homogeneous spaces.

Invariant measures and controllability of finite systems on compact manifolds

Philippe Jouan (2012)

ESAIM: Control, Optimisation and Calculus of Variations

A control system is said to be finite if the Lie algebra generated by its vector fields is finite dimensional. Sufficient conditions for such a system on a compact manifold to be controllable are stated in terms of its Lie algebra. The proofs make use of the equivalence theorem of [Ph. Jouan, ESAIM: COCV 16 (2010) 956–973]. and of the existence of an invariant measure on certain compact homogeneous spaces.

Invariant measures and controllability of finite systems on compact manifolds

Philippe Jouan (2012)

ESAIM: Control, Optimisation and Calculus of Variations

A control system is said to be finite if the Lie algebra generated by its vector fields is finite dimensional. Sufficient conditions for such a system on a compact manifold to be controllable are stated in terms of its Lie algebra. The proofs make use of the equivalence theorem of [Ph. Jouan, ESAIM: COCV 16 (2010) 956–973]. and of the existence of an invariant measure on certain compact homogeneous spaces.

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