OUTPUT CONTROLLABILITY AND OPTIMAL OUTPUT CONTROL OF POSITIVE FRACTIONAL ORDER LINEAR DISCRETE SYSTEM WITH MULTIPLE DELAYS IN STATE, INPUT AND OUTPUT

Mouhcine Naim; Fouad Lahmidi; Abdelwahed Namir

doi:10.11948/20180289

2019 Volume 9 Issue 6

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Mouhcine Naim, Fouad Lahmidi, Abdelwahed Namir. OUTPUT CONTROLLABILITY AND OPTIMAL OUTPUT CONTROL OF POSITIVE FRACTIONAL ORDER LINEAR DISCRETE SYSTEM WITH MULTIPLE DELAYS IN STATE, INPUT AND OUTPUT[J]. Journal of Applied Analysis & Computation, 2019, 9(6): 2169-2189. doi: 10.11948/20180289

Citation:

Mouhcine Naim, Fouad Lahmidi, Abdelwahed Namir. OUTPUT CONTROLLABILITY AND OPTIMAL OUTPUT CONTROL OF POSITIVE FRACTIONAL ORDER LINEAR DISCRETE SYSTEM WITH MULTIPLE DELAYS IN STATE, INPUT AND OUTPUT[J]. Journal of Applied Analysis & Computation, 2019, 9(6): 2169-2189. doi: 10.11948/20180289

OUTPUT CONTROLLABILITY AND OPTIMAL OUTPUT CONTROL OF POSITIVE FRACTIONAL ORDER LINEAR DISCRETE SYSTEM WITH MULTIPLE DELAYS IN STATE, INPUT AND OUTPUT

1.
Laboratory of Analysis, Modeling and Simulation, Faculty of Sciences Ben M'sik, Hassan II University, P.O. Box 7955, Sidi Othman, Casablanca, Morocco
2.
Laboratory of Information Technology and Modeling, Faculty of Sciences Ben M'sik, Hassan II University, P.O. Box 7955, Sidi Othman, Casablanca, Morocco

Corresponding author: Email address: naimmouhcine2013@gmail.com (M. Naim)

Abstract

Abstract

The article concerns output controllability and optimal output control of positive fractional order discrete linear systems with multiple delays in state, input and output. Necessary and sufficient conditions for output reachability (output controllability from zero initial conditions) and null output controllability (output controllability to zero final output) are given and proven. We also prove that the positive system is output controllable if it is output reachable and null output controllable with the output reachability index is equal or less than the null output controllability index. Sufficient conditions for the solvability of the optimal output control problem are given. Numerical examples are presented to illustrate the theoretical results.
- Fractional order /
- positive linear systems /
- output reachability /
- null output controllability /
- output controllability /
- optimal output control
MSC: 93C05, 93C55, 34K35

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References

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