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Controllability and observability for fractional control systems. (English) Zbl 0964.93013
Linear autonomous fractional dynamical control systems are considered. The concepts of controllability and observability in a finite time interval are introduced and discussed. Necessary and sufficient conditions for controllability and observability are formulated and proved using an exact form of the solution to the fractional linear control system. Moreover, the properties of the attainable sets and null controllability domains are investigated using fractional calculus methods. It is shown that the attainable sets are convex and compact and the domains of null controllability are convex and symmetric with respect to the origin. The relations between controllability and observability are also discussed. Similar problems for nonlinear fractional control systems have been recently considered in the paper [{\it A. Abd El-Ghaffar}, {\it M. R. A. Moubarak} and {\it A. B. Shamardan}, Controllability of fractional nonlinear control system, J. Fractional Calc. 17, 59-69 (2000; Zbl 0964.93014)].

26A33Fractional derivatives and integrals (real functions)
93B03Attainable sets
93C10Nonlinear control systems