AN EXTENSION OF T. A. BURTON’S THEOREM

<正> where F:R~+ × C_n~H × C_m~H→ R~n, G:R~+ × C_n~H × C_m~H→ R~m continuous with F(t,0, 0)=0 and G(t,0,0)=0. The present paper shows that in Theorem 1 of [1] the condition of negative definiteness of the derivative of Liapunov functions along the solutions of (1) in state variables (x, y) can be weakened by the condition of negative definiteness in partial state variable y.