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Controllability and observability of the descriptor linear systems reduced to the standard ones by feedbacks

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Kaczorek T. , Klamka J. , Dzieliński A.

Acta Mechanica et Automatica

2024

tom Vol. 18, no. 1

119--122

In this paper, a new method for the reduction of the descriptor linear systems to standards ones is presented and verified. The method uses a state and/or state derivative feedback of output and output derivative feedback in order to transform the descriptor system into a standard one. The controllability and observability properties of the original descriptor as well as transformed standard systems are proved. Simple numerical examples illustrate the theorems introduced.

Controllability of linear convex combination of linear discrete-time fractional systems

100%

Kaczorek T. , Klamka J. , Dzieliński A.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2022

tom Vol. 70, nr 5

art. no. e143102

In this paper the controllability properties of the convex linear combination of fractional, linear, discrete-time systems are characterized and investigated. The notions of linear convex combination and controllability in the context of fractional-order systems are recalled. Then, the controllability property of such a linear combination of discrete-time, linear fractional systems is proven. Further, the reduction of an infinite problem of transition matrix derivation is reduced to a finite one, which greatly simplifies the numerical burden of the controllability issue. Examples of controllable and uncontrollable, single-input, linear systems are presented. The possibility of extension of the considerations to multi-input systems is shown.