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2 International Journal of Applied Mathematics and Computer Science

2 Kaczorek T.

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Analysis of positive linear continuous-time systems using the conformable derivative

Kaczorek T.

International Journal of Applied Mathematics and Computer Science

2018

Vol. 28, no. 2

335--340

Positive linear continuous-time systems are analyzed via conformable fractional calculus. A solution to a fractional linear system is derived. Necessary and sufficient conditions for the positivity of linear systems are established. Necessary and sufficient conditions for the asymptotic stability of positive linear systems are also given. The solutions of positive fractional linear systems based on the Caputo and conformable definitions are compared.

Approximation of fractional positive stable continuous-time linear systems by fractional positive stable discrete-time systems

Kaczorek T.

International Journal of Applied Mathematics and Computer Science

2013

Vol. 23, no. 3

501--506

Fractional positive asymptotically stable continuous-time linear systems are approximated by fractional positive asymptotically stable discrete-time systems using a linear Padé-type approximation. It is shown that the approximation preserves the positivity and asymptotic stability of the systems. An optional system approximation is also discussed.