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Controllability criteria for time-delay fractional systems with a retarded state

Sikora B.

International Journal of Applied Mathematics and Computer Science

2016

Vol. 26, no. 3

521--531

The paper is concerned with time-delay linear fractional systems with multiple delays in the state. A formula for the solution of the discussed systems is presented and derived using the Laplace transform. Definitions of relative controllability with and without constraints for linear fractional systems with delays in the state are formulated. Relative controllability, both with and without constraints imposed on control values, is discussed. Various types of necessary and sufficient conditions for relative controllability and relative U-controllability are established and proved. Numerical examples illustrate the obtained theoretical results.

Pole-assignment for controllable positive linear discrete time systems

Kostova S.

Systems Science

2002

Vol. 28, nr 2

41-50

The aim of this paper is to investigate the relation between controllability and pole-assignment for positive linear discrete-time systems by analogy with nonconstrained systems on the basis of existing in the literature controllability criteria and controllability canonical form. Conditions on the system matrices and closed-loop eigenvalues are presented, which guarantee that there exists a positive feedback matrix with appropriate structure such that the closed-loop system is positive and should have a prescribed set of eigenvalues. The method and procedure for pole-assignment of controllable positive systems are proposed. A numerical example illustrating the procedure is provided.