Control of linear systems using generalized sampled-data hold functions.

*(English)*Zbl 0627.93049The paper presents a problem of T-periodic control system design for MIMO linear time-invariant plants where T is an interval of the synchronous output and input sampling. A periodic single-loop feedback is realized by the choice of the sampled-data hold functions (called GSHF). The period T and a time history of the gains is determined to achieve pole assignment, exact model matching, decoupling and optimal noise rejection. The pole assignment and noise rejection are obtained not only in the single system case but also simultaneously for given N systems. The design procedure is performed under usual controllability and observability assumptions and the gains are functions containing the reachability Gramian on [0,T]. The pole assignment results are valid not only for the discretized system but also for the original closed-loop continuous-time system. Likewise, the above statement is true for the asymptotic stability and simultaneous deadbeat problems. But the model matching, noise rejection and decoupling results based on the Popov invariants pertain only to the discretized system. Although the author presents a robustness stability analysis, it does not allow robustness synthesis directly. In spite of the fact that this paper presents a number of interesting results it does not call out strong feelings one way or the other. It is because although the generalized sampled-data hold functions method enjoys the efficacy of state feedback without the requirement of state estimation, the role and the way of obtaining the hold functions is nothing but state reconstruction in the intersampling time.

Reviewer: A.Swierniak

##### MSC:

93C57 | Sampled-data control/observation systems |

93B35 | Sensitivity (robustness) |

93B55 | Pole and zero placement problems |

93C05 | Linear systems in control theory |