Generalization of Heaviside's Expansion Technique to Transition Matrix Evaluation

The well-known technique of the Heaviside partial fraction expansion is generalized and extended to the state transition matrix determination. The new approach is more convenient than the direct inversion of a square matrix, on one hand, and is much simpler than Sylvester's expansion method, on the other. Two examples (one is a system with distinct roots and one with multiple roots) are included for illustrating the procedures and showing the simplicity of the method.