Since the Lyapunov functional L (t) is nonincreasing, the repetitive application of Theorem 3 at the instants t = kT for k = 0, 1, . . . , p would give L (N(pT )) ? L (N 0 ) ? pc < 0. This is not possible since the Lyapunov functional is always nonnegative ,
, Proposition 5 Fixed k ? N, the solution M(t, ?) of (1) with initial condition M 0 (?) is such that
,
, kT, ?) + ? 2 > 0 such that ? = ? 1 + ? 2 . It is possible to find ? N, with T f = T
, Find T > T 0 big enough (depending on ) such that A(T ? , ·) ? I L ? ? ? 2 and apply the open loop control (u(t), v(t)) = ? T (t)+(?(t),v(t)) to system (1), obtaining M
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