Abstract
A new comparison, extension of Matrozov's approach for the stability analysis of dynamical systems is established.To construct the comparison system vector valued functions whose maximum component is positive definite Instead of vector positive functions are used. In the proposed comparison principle the state vector of the studied system can appear explicitly as a variable in Wazewski's type inequality, thus increasing the flexibility of the approach. Algebraic criteria for uniform asymptotic and exponential stability of nonlinear comparison systems are also established. Finally, a decomposition scheme is proposed to facilitate the application of the method to the stability analysis of large-scale systems.
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