Controllability of nonlinear fractional dynamical systems

Controllability, reachability and minimum energy control of fractional discrete-time linear systems with multiple delays in state

“…The problems of controllability and reachability of dynamic systems, standard and fractional, have been recently considered in many papers (see [3][4][5][6][7][8][9][10][11][12][13], for example). A survey of recent results in theory of controllability of dynamical systems is given in [14].…”

“…where Q is a symmetric positive definite weighting matrix of the performance index (11). The matrix W defined by (46) is non-singular if and only if the matrix R N has full row rank.…”

“…transfers the system (1) from zero initial conditions to the final state x f ∈ ℜ n and minimises the performance index (11). Moreover, the minimal (optimal) value of this index is given by…”

The controllability of nonlinear implicit fractional delay dynamical systems

“…Bettayeb and Djennoune (2008) established new results on the controllability and observability of fractional dynamical systems. The controllability of nonlinear fractional dynamical systems was studied by Balachandran et al (2012b) using the fixed point argument. Fractional order differential equations with delay in the state variable have recently proved to be a valuable tool in the modeling of many phenomena in various fields.…”

Stabilizability of fractional dynamical systems

“…The problem of controllability of linear systems represented by fractional differential equations in finite dimensional spaces has been extensively studied by many authors [1,12,21]. Balachandran et al [6,7,8,9, 10] established sufficient conditions for the controllability of nonlinear fractional dynamical systems with or without delays in finite dimensional spaces using fixedpoint techniques. More recently, controllability of higher order nonlinear fractional dynamical systems are also studied by Balachandran et al [4,5].…”