| Since 1970s, large-scale system models have been applied to the realm of engineering technology, economy and ecology since the extension of system space and the complication of system structure. A more deep investigation on the robust stability for linear uncertain interconnected large-scale systems with time-delays not only perfects the foundation of control theory, but also promotes the implementation of such theory in practice. This paper mainly discusses the robust stability for linear uncertain interconnected large-scale systems with constant time-delays and varying time-delays. Some results of large-scale systems with time-delays are extended to interconnected large-scale systems with uncertainty, and M matrix and linear matrix inequality method are applied to the investigation of the robust stability for linear uncertain interconnected large-scale systems. Main results of this paper include the following three parts: 1. The problem of robust stability is studied for the uncertain interconnected large-scale systems with constant time-delays. Under high structured uncertainty, unstructured uncertainty and matrix polytope structured uncertainty assumptions, the sufficient conditions of robust stability are derived by using Lyapunov function and Razumikhin theorem. Some examples are given to illustrate them. 2. The robust stability for the uncertain interconnected large-scale systems with constant time-delays is studied. We give the sufficient conditions of robust stability for high structured uncertainty and unstructured uncertainty assumptions based on Lyapunov functional method and the properties of M matrix. 3. The problem of robust stability is studied for the uncertain interconnected large-scale systems with varying time-delays. The sufficient conditions of robust stability are derived under high structured uncertainty, matrix polytope structured uncertainty and norm bounded uncertainty by using Lyapunov function and LMI method. All the principles are time-delay independent.
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