Controllability of Linear Time Varying Systems: New Algebraic Criteria

This paper presents algebraic rank conditions for the complete controllability of the system x¿(t) = A(t)x(t) + Bu(t) = ¿^mi=1 ai(t)Aix(t) + Bu(t). x R^x, u R^l. Assuming A(.) is locally integrable on R, the fundamental solution of x¿(t) = A(t)x(t) is explicity calculated in terms of functions ai(t) for t [0,T] by using Lie algebra theory. Then by using the Cayley-Hamilton theorem, two diffierent time invariant controllability matrices are derived. Conditions for complete controllability of the above systems are derived in terms of the rank of these matrices.