A parameter imbedding solution of algebraic matrix riccati equation

Abstract

An imbedding solution for the matrix Riccati equation is presented in this paper. One or all of the system’s matrices is first imbedded by introducing a parameter ∈, 0 ≤ ∈ 1 and then taking a total derivative of the Riccati equation which provides a Lyapunov equation. Making use of the solution of the latter equation the Riccati matrix is obtained by an integration in the space of the parameter ∈. The method can handle both stable and unstable systems. Three numerical examples illustrate the method, its imbedding scheme, and comparison with the exact and another iterative technique. The results show that for the cases where an approximate solution to the Riccati equation is needed, the method is rather attractive in both accuracy and speed. Very cheap solutions can be found with reasonable accuracy. For a fifteenth-order system, a solution within 0·4% of the exact answer was obtained in 30 sec on the HP-2100 computer. © 1977 Taylor and Francis Group, LLC.