The stability for the hyperneutral type nonlinear time varying control systems (1)

We discuss the equivalence problem of hyperneutral type nonlinear time varying control system and linear time varying control system in the theory of stabilization. Making use of the symmetric positive definite solution of Riccati matrix differential equation which corresponds to the linear time varying control system, we construct the Lyapunov function. Then we provide the sufficent conditions which make that the zero solution of the hyperneutral type nonlinear time varying control systems is uniformly asymptotically stable by means of the Lyapunov equivalence decomposition method, and find the formulaes which can be used to estimate the bounds of the time delays and the nonlinear terms. Mong Peiyuan: born in 1950, Associate professor Supported by the Natural Science Foundation of Hubei Province Education Committee. Project code: 97A080