Construction of Lyapunov functions from a class of forms of power $2p$ for the study of absolute stability of control systems with nonstationary nonlinear elements

For the problem of absolute stability of control systems whose elements are nonstationary and nonlinear a procedure is proposed whereby a Lyapunov function of phase variables is obtained from a class of forms of power $2p$ through nonlinear transformation of the system phase coordinates and the numerical method [1] of designing Lyapunov functions from the class of quadratic forms. A case study demonstrates improvement of estimates of the parametric stability region over what is obtained by the widespread circular criterion of absolute stability.