Advantages of the State Space Matrix Approach

The state-space approach requires an additional operation to perform the matrix inversion (or an LU-decomposition). Despite the complexity, the state-space method presents an elegant approach for ODE’s.

The form of the higher order ODE’s gets converted into 1^st order ODE’s, which can easily and readily be applied to any numerical solver. The state-space condensed matrix allows one to visualize the original nature of the problem (in K, C & M for the mass-spring-damper system). In other words, from an algorithmic stand point, all one needs to supply is the coefficient matrices along with the forcing functions and not worry about conversions to an equivalent format.

For a series of equations of higher order, the state-space method is thus more effective once the initial definition of the matrix is derived.