Weighted least squares stationary approximations to linear systems
GERALD J. BIERMAN · IEEE Transactions on Automatic Control · 1972
The problem of replacing the time-varying linear system\dot{X} = A(t)Xby a stationary one\dot{Y} = BYis investigated. The matrixBis selected so thatX(t) = Y(t)in the interval [0, T]. Several quadratic criteria are proposed to aid in determining suitable candidate systems. One criterion for choosingBis initial condition dependent, and another bounds the "worst case" homogeneous system performance. Both of these criteria produce weighted least squares fits toA(t).