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Bézout factors and \(L^1\)-optimal controllers for delay systems using a two-parameter compensator scheme. (English) Zbl 0959.93052

The robust control for a class of linear delay systems of the form \[ \dot x(t)= \sum^k_{i=0} A_ix(t- t_i)+ \sum^m_{i=0} B_iu(t- \tau_i), \]
\[ y(t)= \sum^l_{i=0} C_ix(t- \sigma_i)+ \sum^p_{i=0} d_i u(t-v_i) \] is discussed by using a frequency-domain approach which considers the parametrized controllers \[ C= (X+ DN)(Y+ NQ)^{-1}, \] where \(X\), \(Y\) are the Bézout factors of the plant \(G(s)\). It is shown that these Bézout factors can be chosen to be continuous in the gap topology with respect to variations of the coprime factors. The \(L^1\)-optimal tracking problem is solved simultaneously with optimal robust stabilization.

MSC:

93D21 Adaptive or robust stabilization
93C23 Control/observation systems governed by functional-differential equations
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