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This paper presents new algorithms for the scheduling and allocation phases in high-level synthesis under time and resource constraints. This is achieved by formulating these problems in terms of Liapunov's stability theorem using a transformation technique between the design space and the dynamic system space. These algorithms are based on moves in the design space, which correspond to the moves toward the equilibrium point in the dynamic system space. The scheduling algorithm (MFS) takes care of mutually exclusive operations, loop folding, multicycle operations, chained operations, and pipelining (structural and functional). The mixed scheduling-allocation algorithm (MFSA) can handle all of the above scheduling applications as well as simultaneously performing allocation of functional units, registers, and interconnects while minimizing the overall cost.