A New Numerical Solution of Xͦ=A1X+XA2+D, X(0) = C

Abstract

Another numerical solution of the general matrix differential equation Xͦ = A1X + XA2 + D, X(0)=C for X is considered without any stability condition for A1 and A2. Like Davison's method, the proposed algorithm requires only some n2 words of memory and n3 multiplications where n = max(n1,n2) and A ϵ Rn1×n1, A2ϵ Rn2×n2. This new approach is well suited to solve large and possibly unstable systems. We take the opportunity to run the differential equation for various D. A very efficient technique follows to design the so-called receding horizon control problem. Copyright © 1977 by The Institute of Electrical and Electronics Engineers, Inc.