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This paper develops finite-time consensus theory for multi-agent systems and presents the design and analysis results of distributed consensus protocols, which are continuous state feedbacks. Those distributed algorithms are in general form and have their wide range of applications, including fast consensus, saturation control, and network connectivity preserving. By employing the tools of finite-time Lyapunov theory and algebraic graph theory, we present the relaxable interaction-topology conditions that can guarantee the solvability of finite-time consensus problems. Specific examples are given to demonstrate the applications of our theoretical results.