Abstract

    For a linear time varying (LTV) system contain-ing stable and unstable modes, the paper gives the necessary and sufficient conditions for asymptotic decoupling of stable modes. Establishment of the conditions relies on newly developed techniques for analyzing matrix exponential and state transition matrix. The research exploits fundamental properties of LTV systems and advances the knowledge base of linear control theory. The results can find a direct application in the autonomous synchronization problem for heterogeneous multi-agent systems. The research methodology is based on rigorous theoretical proofs and numerical verification.