A negative exponential solution for the matrix Riccati equation

A new form is presented for the transient solution of the matrix Riccati equation associated with the linear optimal regulator and filter problems for time-invariant plants. The solution is expressed in a form such that the transient terms decay exponentially with time, leaving the steady-state terms. In contrast to the automatic synthesis program (ASP) matrix iteration method, the negative exponential solution does not code essential information in numbers of widely differing magnitudes.