z-transform techniques are employed to establish general symmetry and simultaneity properties of the first sensitivity functions of the phase-canonical form of single-input, nth-order, linear, constant, discrete-time, controllable systems. It is demonstrated that computation of the first sensitivity function requires one nth-order model in addition to the system model. This simultaneity property is extended to arbitrary single-input, nth-order, linear, constant, discrete systems. In complete analogy with results presented for continuous systems, symmetry and simultaneity properties may be established for the computation of the /th sensitivity function \begin{equation*}^{l}\beta^{y} \triangleq \frac{\partial^{l}y_{i}}{\partial\alpha_{Jl}\partial\alpha_{Jl-1}\cdots\partial\alpha_{J2}\partial\alpha_{J1}}|_{\alpha=\alpha_{0}} {\rm for} \substack{i = 1,2,\ldots,n\\ J_{k} = 1,2,\ldots,n\\ k = 1,2,\ldots,l.}\end{equation*} Extension of these results to multi-input systems is also mentioned. The usefulness of the simultaneity property is illustrated by applying the results to the design of a low-sensitivity optimal control law.


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    Titel :

    Sensitivity Functions for Linear Discrete Systems with Applications


    Beteiligte:

    Erschienen in:

    Erscheinungsdatum :

    01.11.1972


    Format / Umfang :

    1667591 byte




    Medientyp :

    Aufsatz (Zeitschrift)


    Format :

    Elektronische Ressource


    Sprache :

    Englisch