Controllability

• Controllability: (*A,B*) is controllable if, for any initial state

continuous) input *u(.)* such that *x(t**1**) = x**1*.

• The matrix

is positive definite for any *t* > 0.

• The controllability matrix *C*=[*B AB A*2*B … A*n-1*B*]

has full row rank, i.e.,

•The
eigenvalues of *A+BF* can be freely assigned by a

suitable F.