Model reduction of unstable systems using balanced truncation method and its application to shallow water equations

Abstract

In this paper, we discuss the reduction of unstable systems. Suppose we have a large-scale unstable system. The reduction of such systems are done in order to obtain a simpler model that has a similar behavior with the original model. In reality, a higher order model is not preferred because the computation takes more time. Thus we need a method to reduce the order of a model that is known as model reduction. Model reduction of a system is the method of approximation of a system with a lower order but the dynamic behavior is equal or almost equal to the original model. In this paper, we discuss model reduction of unstable systems. Finally this method is applied to shallow water equation that describes the flow of water in rivers: we obtain a procedure for model reduction of unstable systems and the reduced model of shallow water equations.