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The classical Cayley-Hamilton theorem is extended to Drazin inverse matrices. A new procedure based on this extension for computation of the Drazin inverse matrices is proposed.
The classical Cayley-Hamilton theorem is extended to the fractional descriptor continuous-time linear systems. First the theorem is extended to fractional descriptor linear systems with commuting matrices and next to any pair of matrices of the descriptor linear systems. The extensions are based on the application of the Lagrange-Sylvester formula of the function of matrices.
The problem of existence of reachable pairs (A, B) of discrete-time linear systems is formulated and solved. Necessary and sufficient conditions for the reachability of standard and positive full order and fractional order discrete-time linear systems are recalled. The existence of the reachable pairs (A, B) of the systems is investigated. Considerations are illustrated by numerical examples.
Necessary and sufficient conditions for the positivity and reachability of electrical circuits composed of resistors, coils and capacitors are given. The minimum energy control problem for the positive electrical circuits is formulated and solved. Procedure for computation of the optimal input and minimal value of the performance index is proposed and illustrated by a numerical examples.
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