Input-output and state-space representations of finite-dimensional linear time-invariant systems

AbstractIn this paper we develop various representations for systems described by aset of high-order differential equations of the form R0w + R1w + … + Rsw(s) = 0, with R0, R1,…, Rs not necessarily square matrices. The variables w are the external variables. Particular attention is paid to the problem of obtaining minimal state-space realizations and input-output or input-state-output representations of such systems