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Computation of controllability and observability Gramians in modeling of discrete‐time noncommensurate fractional‐order systems
Author(s) -
Rydel Marek,
Stanisławski Rafał
Publication year - 2020
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.2060
Subject(s) - observability , controllability , mathematics , computation , integer (computer science) , fractional order system , control theory (sociology) , state space , discrete time and continuous time , mathematical optimization , dimension (graph theory) , model order reduction , computer science , fractional calculus , algorithm , projection (relational algebra) , statistics , control (management) , artificial intelligence , programming language , pure mathematics
This paper presents a new algorithm for computation of controllability and observability Gramians for an expanded state space form of integer‐order approximator to linear time‐invariant discrete‐time noncommensurate fractional‐order systems. The introduced methodology can significantly reduce the time complexity of the Gramians' calculation, being the main computational burden in modeling of discrete‐time fractional‐order systems by means of a high integer‐order expanded state space approximator and the balanced truncation reduction method. Simulation experiments illustrate an efficiency of the introduced methodology, in particular for low‐dimension fractional‐order systems and high implementation lengths.