Controlabilidade de sistemas de controle lineares - João Augusto Navarro Cossich (2015)
In this work, we studied the general results about control systems on a smooth manifold M , that is, a family of differential equations x?(x) = X(x(t), u(t)) on M , where u : R ? U ? Rm belongs to a function set U which we impose some weak regularities, X : M × Rm ? TM is a C1 map such that for each u ? U , the function Xu : M × TM is a vector field on M. After that we present the control set notion, which is really important to study the controllability of general control sistems, in particular the non linear cases. Finally, we show the main results about the controllability of linear control systems on Rd, which are a particular and very interesting class of control systems. The map X is given by X(x, u) = Ax + Bu, where A ? Rd×d and B ? Rd×m