Computation of controllability and observability Gramians in modeling of discrete‐time noncommensurate fractional‐order systems

2019 ◽  
Vol 22 (3) ◽  
pp. 1052-1064
Author(s):  
Marek Rydel ◽  
Rafał Stanisławski
Keyword(s):  
Fractional Order ◽  
Discrete Time ◽  
Fractional Order Systems ◽  
Controllability And Observability

scholarly journals Controllability and Observability of Linear Discrete-Time Fractional-Order Systems

2008 ◽  
Vol 18 (2) ◽  
pp. 213-222 ◽  
Author(s):  
Said Guermah ◽  
Said Djennoune ◽  
Maamar Bettayeb
Keyword(s):  
Structural Properties ◽  
Fractional Order ◽  
Discrete Time ◽  
Analytical Methods ◽  
Fractional Order Systems ◽  
Numerical Examples ◽  
New Concepts ◽  
Controllability And Observability ◽  
Theoretical Results

Controllability and Observability of Linear Discrete-Time Fractional-Order SystemsIn this paper we extend some basic results on the controllability and observability of linear discrete-time fractional-order systems. For both of these fundamental structural properties we establish some new concepts inherent to fractional-order systems and we develop new analytical methods for checking these properties. Numerical examples are presented to illustrate the theoretical results.

Local controllability of nonlinear discrete-time fractional order systems

2013 ◽  
Vol 61 (1) ◽  
pp. 251-256 ◽  
Author(s):  
D. Mozyrska ◽  
E. Pawłuszewicz
Keyword(s):  
Linear Approximation ◽  
Fractional Order ◽  
Discrete Time ◽  
Local Controllability ◽  
Difference Operators ◽  
Fractional Order Systems ◽  
Discrete Time System ◽  
Controllability Problem ◽  
Time System ◽  
Order Difference

Abstract The Riemann-Liouville, Caputo and Gr¨unwald-Letnikov fractional order difference operators are discussed and used to state and solve the controllability problem of a nonlinear fractional order discrete-time system. It is shown that independently of the type of fractional order difference, such a system is locally controllable in q steps if its linear approximation is globally controllable in q steps

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