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

scholarly journals Chaos and control of a three-dimensional fractional order discrete-time system with no equilibrium and its synchronization

AIP Advances ◽  
2020 ◽  
Vol 10 (4) ◽  
pp. 045310 ◽  
Author(s):  
Adel Ouannas ◽  
Amina Aicha Khennaoui ◽  
Shaher Momani ◽  
Giuseppe Grassi ◽  
Viet-Thanh Pham
Keyword(s):  
Fractional Order ◽  
Discrete Time ◽  
Three Dimensional ◽  
Discrete Time System ◽  
Time System ◽  
And Control

Stability analysis of a discrete-time system with a variable-, fractional-order controller

2010 ◽  
Vol 58 (4) ◽  
pp. 613-619 ◽  
Author(s):  
P. Ostalczyk
Keyword(s):  
Stability Analysis ◽  
Fractional Order ◽  
Discrete Time ◽  
Closed Loop ◽  
Control Strategies ◽  
Discrete Time System ◽  
Time System ◽  
Matrix Condition Number ◽  
Fractional Order Controller ◽  
Matrix Condition

Stability analysis of a discrete-time system with a variable-, fractional-order controllerVariable, fractional-order backward difference is a generalisation of commonly known difference or sum. Equations with these differences can be used to describe a variable-, fractional order digital control strategies. One should mention, that classical tools such as a state-space description and discrete transfer function cannot be used in the analysis and synthesis of such a type of systems. Equations describing a closed-loop system are proposed. They contain square matrices imitating the action of matrices in the system polynomial matrix description. This paper focuses on the stability analysis of a closed-loop SISO linear system with a controller described by the equations mentioned. A stability condition based on a transient denominator matrix condition number is proposed. Investigations are supported by two numerical examples.

A New Method for Discrete-Time System Reduction

1988 ◽  
Author(s):  
Ioannis S. Apostolakis ◽  
John Diamessis ◽  
David Jordan
Keyword(s):  
Discrete Time ◽  
New Method ◽  
Discrete Time System ◽  
Time System ◽  
System Reduction

On a Discrete-Time System Expressed in the Euler Operator

1988 ◽  
Author(s):  
Noriyuki Hori ◽  
Peter N. Nikiforuk ◽  
Kimio Kanai
Keyword(s):  
Discrete Time ◽  
Discrete Time System ◽  
Time System ◽  
Euler Operator
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