Acta mathematica scientia,Series B ›› 2015, Vol. 35 ›› Issue (5): 1003-1013.doi: 10.1016/S0252-9602(15)30034-5

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CONTROLLABILITY AND OPTIMALITY OF LINEAR TIME-INVARIANT NEUTRAL CONTROL SYSTEMS WITH DIFFERENT FRACTIONAL ORDERS

Xiaoli DING1, Juan J. NIETO2,3   

  1. 1. Department of Mathematics, Xi'an Polytechnic University, Xi'an 710048, China;
    2. Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15782, Santiago de Compostela, Spain;
    3. Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia
  • Received:2014-05-13 Revised:2014-07-27 Online:2015-09-01 Published:2015-09-01
  • Contact: Xiaoli DING E-mail:dingding0605@126.com
  • Supported by:

    The first author is supported by the Science and Technology Planning Project (2014JQ1041) of Shaanxi Province and the Scientic Research Program Funded by Shaanxi Provincial Education Department (14JK1300) and the Research Fund for the Doctoral Program (BS1342) of Xi'an Polytechnic University. The second author is partially supported by Ministerio de Economíay Competitividad and EC fund FEDER, Project no. MTM2010-15314, Spain.

Abstract:

Control systems governed by linear time-invariant neutral equations with different fractional orders are considered. Sufficient and necessary conditions for the controllability of those systems are established. The existence of optimal controls for the systems is given. Finally, two examples are provided to show the application of our results.

Key words: controllability, optimality, neutral equations, different fractional orders

CLC Number: 

  • 26A33
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