SIAM Journal on Control and Optimization, Volume 58, Issue 4, Page 2114-2142, January 2020.
Unlike output-controllability of linear systems which is a consequence of controllability, the output-controllability problems of nonlinear systems can be much more difficult than the controllability problems. Thus, it is a challenging task to derive criteria, especially algebraically verifiable ones, for output-controllability of nonlinear systems. In this paper, we consider output-controllability of a class of fundamental driftless discrete-time bilinear systems. We show that output-controllability of such systems cannot be fully deduced by controllability; however, near-controllability plays a key role in studying the output-controllability problem. A general necessary and sufficient condition as well as an algebraically verifiable sufficient condition is obtained for output-controllability of the systems via near-controllability. Our study reveals that output-controllability of a nonlinear system needs to be determined by its near-controllability instead of its controllability. Furthermore, inspired by near-controllability, we introduce a new notion, called output-near-controllability, for nonlinear systems and demonstrate it on the bilinear systems. Necessary as well as sufficient algebraic conditions for output-near-controllability of the bilinear systems are presented. Examples are given to demonstrate the conceptions and results of this paper.

中文翻译：

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无漂移离散双线性系统的输出可控性和输出近可控性

SIAM控制与优化杂志，第58卷，第4期，第2114-2142页，2020年1月。
不同于线性系统的输出可控制性是可控制性的结果，非线性系统的输出可控制性问题比可控制性问题要困难得多。因此，为非线性系统的输出可控制性导出标准，尤其是代数可验证的标准是一项艰巨的任务。在本文中，我们考虑了一类基本的无漂移离散时间双线性系统的输出可控制性。我们表明，这种系统的输出可控性不能完全由可控性推论得出。然而，近可控性在研究输出可控性问题中起着关键作用。通过接近可控制性获得了系统的输出可控制性的一般必要和充分条件以及可代数验证的充分条件。我们的研究表明，非线性系统的输出可控制性需要由其近可控制性而不是其可控制性来确定。此外，受近可控制性的启发，我们为非线性系统引入了一种称为“输出接近可控制性”的新概念，并在双线性系统上进行了演示。给出了双线性系统输出附近可控性的必要及充分代数条件。举例说明了本文的概念和结果。给出了双线性系统输出附近可控性的必要及充分代数条件。举例说明了本文的概念和结果。给出了双线性系统输出附近可控性的必要及充分代数条件。举例说明了本文的概念和结果。