Rational approximation of L/sub 1/ optimal controllers for SISO systems

The L/sub 1/ optimal control problem with rational controllers for continuous-time systems is considered in which it is shown that the optimal L/sub 1/ performance index with rational controllers is equal to that of irrational controllers. A sequence of rational controllers that approximates the optimal index is constructed. Convergence properties of such a sequence are studied. That the corresponding sequence of objective transfer functions is shown to converge in weak-* topology in BV(R/sub +/) in the time domain and uniformly in a wider sense in the frequency domain.<
>