Lyapunov functions that specify necessary and sufficient conditions of absolute stability of nonlinear nonstationary control systems. III (Q581338)

[For part I and II, see the authors, Avtom Telemekh. 1986, No.3, 63-73 (1986; Zbl 0607.93039), and ibid., No.4, 5-15 (1986; Zbl 0618.93051), resp.] Necessary and sufficient condition for absolute stability in terms of the solvability of a system of matrix equations are obtained for nonlinear control systems with several nonstationary nonlinearities that satisfy sector constraints. After that, necessary and sufficient conditions for asymptotic stability are similarly obtained for linear stationary systems and for a special class of differential inclusions.