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首页> 外文期刊>IEEE Transactions on Automatic Control >Losslessness, feedback equivalence, and the global stabilization ofdiscrete-time nonlinear systems
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Losslessness, feedback equivalence, and the global stabilization ofdiscrete-time nonlinear systems

机译：离散非线性系统的无损，反馈等效和全局稳定

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摘要

In this paper a necessary and sufficient condition for a nonlinear system of the form Σ, given by x(k+1)=f(x(k))+g(x(k))u(k), y(k)=h(x(k))+J(x(k))u(k), to be lossless is given, and it is shown that a lossless system can be globally asymptotically stabilized by output feedback if and only if the system is zero-state observable. Then, we investigate conditions under which Σ can be rendered lossless via smooth state feedback. In particular, we show that this is possible if and only if the system in question has relative degree {0,...,0} and has lossless zero dynamics. Under suitable controllability-like rank conditions, we prove that nonlinear systems having relative degree {0,...,0} and lossless zero dynamics can be globally stabilized by smooth state feedback. As a consequence, we obtain sufficient conditions for a class of cascaded systems to be globally stabilizable. The global stabilization problem of the nonlinear system Σ without output is also investigated in this paper by means of feedback equivalence. Some of the results are parallel to analogous ones in continuous-time, but in many respects the theory is substantially different and many new phenomena appear
机译：本文针对Σ形式的非线性系统的充要条件，由x（k + 1）= f（x（k））+ g（x（k））u（k），y（k）给出= h（x（k））+ J（x（k））u（k）是无损的，并且表明，当且仅当该系统为无损系统时，该无损系统可以通过输出反馈全局渐近稳定化。零状态可观察。然后，我们研究了可以通过平滑状态反馈使Σ无损的条件。特别是，我们证明只有当所讨论的系统具有相对度{0，...，0}并且具有无损零动态时，这才有可能。在合适的类似于可控制性的秩条件下，我们证明具有相对度{0，...，0}和无损零动力学的非线性系统可以通过平滑状态反馈来全局稳定。结果，我们获得了使一类级联系统全局稳定的充分条件。本文还通过反馈等效性研究了无输出的非线性系统Σ的全局稳定问题。一些结果在连续时间内与类似结果平行，但在许多方面，该理论有很大不同，并且出现了许多新现象。

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