Stability of nonlinear switched systems is discussed. A method of constructing the common (scalar and vector) Lyapunov functions is proposed for switched systems whose equations have homogenous right-hand sides and for switched large-scale systems containing homogeneous subsystems. With the aid of homomorphic mapping the problem of stability for nonhomogeneous nonlinear systems is reduced to an auxiliary problem, which is easier to analyze. Matrix homomorphism is used for the purpose of ellipsoidal estimation of nonlinear dynamics of the polynomial class of systems. Certain applications are mentioned.
