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Full-order observers for linear fractional multi-order difference systems

Wyrwas M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2017

Vol. 65, nr 6

891--989

The paper is devoted to the construction of observers for linear fractional multi–order difference systems with Riemann–Liouville– and Grünwald–Letnikov–type operators. Basing on the Z-transform method the sufficient condition for the existence of the presented observers is established. The behaviour of the constructed observer is demonstrated in numerical examples.

Asymptotic behaviour of real two-dimensional differential system with a finite number of constant delays

Rebenda J.

Demonstratio Mathematica

2008

Vol. 41, nr 4

845-857

In this article stability and asymptotic properties of a real two-dimensional system x'(t) = A(t)x(t) +[...]=i Bj(t)x(t - r j) + h(t, x (t), x (t - n), ...,x(t- rn)) are studied, where r1 > 0,..., rn > 0 are constant delays, A, B1, ..., Bn are the matrix functions and h is the vector function. Generalization of results on stability of a two-dimensional differential system with one constant delay is obtained using the methods of complexification and Lyapunov-Krasovskii functional and some new corollaries and an example are presented.

Oscillatory properties of solutions of neutral differential systems

Spanikova E.

Fasciculi Mathematici

2001

Nr 31

91-103

The purpose of this paper is to obtain oscillation criterions for the neutral differential systems (S).

Hyperbolic transformation and hyperbolic difference systems

Dosly O., Pospisil Z.

Fasciculi Mathematici

2001

Nr 32

25-48

Transformations of symplectic difference systems (mathematical formula) are investigated. It is shown that symplectic systems satisfying certain additional condition can be transformed (using a transformation that preserves oscillation properties of transformed systems) into the so-called hyperbolic difference system. Basic properties of solutions of hyperbolic systems are established.