---

Journal of Applied Nonlinear Dynamics 1(2) (2012) 195--205 | DOI:10.5890/JAND.2012.05.006

Zbigniew Zaczkiewicz

Faculty of Computer Science, Bialystok University of Technology, Bialystok, Poland

Download Full Text PDF

 

Abstract

The paper deals with problems of relative controllability and Rn1 - observability for linear stationary fractional differential-algebraic system with delay (FDAD). FDAD system consists of fractional differential in the Caputo sense and difference equations. We present control systems and observation systems. We introduce the determining equation systems and their properties. By solution representations into series of their determining equation solutions we obtain effective parametric rank criteria for relative controllability and Rn1 -observability. A dual controllability result is also formulated.

Acknowledgments

This research was supported by Bialystok University of Technology (grant no. S/WI/2/11).

References

1. [1]	Kilbas A. A., Srivastava H. M., Trujillo J. J., (2007), Theory and Applications of fractional Differential Equations, 4th ed., Springer, Berlin.

2. [2]	Kaczorek T. (2011), Selected Problems of Fractional Systems Theory, Springer-Verlag GmbH, Berlin.

3. [3]	Marchenko V. M., Poddubnaya O. N. (2004), Relative controllability of stationary hybrid systems, in Proc. IEEE Methods and Models in Automation and Robotics (MMAR 2004), Miedzyzdroje, Poland, 267–272.

4. [4]	Marchenko V. M., Poddubnaya O. N. (2002), Expansion of hybrid control systems solutions into series of their determining equation solutions, Cybernetics and computer techniques, 135, 39–49.

5. [5]	Marchenko V. M., Poddubnaya O. N., Zaczkiewicz Z. (2006), On the observability of linear differential-algebraic systems with delays, IEEE Trans. Automat. Control., 51(8), 1387-1392.

6. [6]	Zaczkiewicz Z. (2010), Representation of solutions for fractional differential-algebraic systems with delays, Bulletin of the Polish Academy Of Sciences Technical Sciences, 58(4), 607–612.