Second-Order State-Space Formulation of Systems

A method of describing systems by sets of second-order differential equations is suggested. In this second-order state-space formulation the states are defined in a manner slightly different from the conventional one. It is shown that this modified procedure reduces the order of matrices, renders easier the evaluation of the characteristic equation and the system solution, and provides some additional insight into the relative stability of system states. Procedures of characterization and analysis of systems by this modified method are indicated, and an example is considered to illustrate the advantageous features of the method in contrast with the normal procedure. © 1970 IEEE