• Controllability: (A,B) is controllable if, for any initial state
x(0)=x0, t1>0 and final state x1, there
exists a (piecewise
continuous) input u(.) such that x(t1) = x1.
• The matrix
is positive definite for any t > 0.
• The controllability matrix C=[B AB A2B … An-1B]
has full row rank, i.e.,
•The
eigenvalues of A+BF can be freely assigned by a
suitable F.