POLYSTABILITY - A NEW DIRECTION IN THE ANALYSIS OF NONLINEAR-SYSTEMS (SURVEY)

This article examines the general problem of the polystability of moti on of nonlinear and nonautonomous systems. The problem of polystabilit y is a generalization of the classical stability problem of A. M. Lyap unov. New theorems on polystability are proposed on the basis of speci al Lyapunov matrix functions. Two approaches are developed, the first. involving the construction of a scalar function on the basis of matri x functions. The second approach entails the construction of a vector function and employs a variant of the comparison method developed espe cially for the given problem. Systems consisting of two, three, and fo ur subsystems are discussed in succession. The problem of the polystab ility of a winged aircraft is examined as an example.