Decomposition of descriptor fractional linear systems into dynamic and static parts
- KACZOREK Tadeusz
- Kategoria: Pozostałe zagadnienia
A method for decomposition of descriptor fractional linear systems with regular pencils into dynamic and static parts is proposed. The method is based on modified version of the shuffle algorithm. A procedure of the decomposition is given and illustrated on numerical examples.
1. INTRODUCTION
Descriptor (singular) linear systems have been addressed in many papers and books [14, 7, 8, 12]. The eigenvalues and invariants assignment by state and output feedbacks have been investigated in [1-3, 6, 12] and the realization problem for singular positive continuous-time systems with delays in [10]. The computation of Kronecker’s canonical form of a singular pencil has been analyzed in [15].The fractional differential equations have been considered in the monograph [14]. Fractional positive linear systems have been addressed in [5, 9] and in the monograph [11]. Luenberger in [13] has proposed the shuffle algorithm to analysis of the singular linear systems.
In this paper a method for decomposition of the descriptor fractional linear systems with regular pencils into dynamic and static parts will be proposed. The method is based on the modified version of the shuffle algorithm.
The paper is organized as follows. In section 2 the decomposition method is presented for descriptor fractional discrete-time linear system. In section 3 the method is extended to the descriptor fractional continuous-time linear systems. Concluding remarks are given in section 4.
To the best of the author’s knowledge the decomposition of descriptor fractional linear systems into dynamic and static parts has not been considered yet. (...)
Descriptor (singular) linear systems have been addressed in many papers and books [14, 7, 8, 12]. The eigenvalues and invariants assignment by state and output feedbacks have been investigated in [1-3, 6, 12] and the realization problem for singular positive continuous-time systems with delays in [10]. The computation of Kronecker’s canonical form of a singular pencil has been analyzed in [15].The fractional differential equations have been considered in the monograph [14]. Fractional positive linear systems have been addressed in [5, 9] and in the monograph [11]. Luenberger in [13] has proposed the shuffle algorithm to analysis of the singular linear systems.
In this paper a method for decomposition of the descriptor fractional linear systems with regular pencils into dynamic and static parts will be proposed. The method is based on the modified version of the shuffle algorithm.
The paper is organized as follows. In section 2 the decomposition method is presented for descriptor fractional discrete-time linear system. In section 3 the method is extended to the descriptor fractional continuous-time linear systems. Concluding remarks are given in section 4.
To the best of the author’s knowledge the decomposition of descriptor fractional linear systems into dynamic and static parts has not been considered yet. (...)
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Źródło: Czasopismo Logistyka
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