On the principle of linearized stability for nonlinear hyperbolic systems

The principle of linearized stability is proved to be valid for a class of hyperbolic nonlinear systems. One example in fluid mechanics is worked out to show how the principle is applied for determining the local stability of its stationary solution. The example is concerned with the irrigation canal system governed by the Saint Venant equation. The principle of linearized stability should be useful in the construction of stabilizing feedback laws for networks of irrigation canals.