Abstract
This paper is concerned with the controllability and observability for a class of fractional linear systems with two different orders. The sufficient and necessary conditions for state controllability and state observability of such systems are established. The results obtained extend some existing results of controllability and observability for fractional dynamical systems.
Highlights
In the last three decades, interest in fractional calculus has experienced rapid growth and at present we can find many papers devoted to its theoretical and application aspects; see the work of [1] and the references therein
During recent years a renewed interest has been devoted to fractional order systems in the area of automatic control; the reader can refer to monograph [10]
Fractional order control is the use of fractional calculus in the aforementioned topics, the system being modeled in a classical way or as a fractional one
Summary
In the last three decades, interest in fractional calculus has experienced rapid growth and at present we can find many papers devoted to its theoretical and application aspects; see the work of [1] and the references therein. Shamardan and Moubarak [20] extended some basic results on the controllability and observability of linear discrete-time fractional order systems and developed some new concepts inherent to fractional order systems with analytical methods for checking their properties. In recent paper [22], necessary and sufficient conditions of controllability and observability for fractional linear time invariant system are included. To the best of our knowledge, there has been no result about the controllability and observability of fractional linear systems with different orders. We derive the sufficient and necessary conditions on controllability and observability for the fractional linear systems with two different orders. The main results about controllability and observability for the fractional linear systems with two different orders are given in.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
