### Positive-Controllability, Positive-Near-Controllability, and Canonical Forms of Driftless Discrete-Time Bilinear Systems

TIE Lin

1. School of Automation Science and Electrical Engineering, Beihang University, Beijing 100083, China
• Received:2020-12-24 Revised:2021-07-05 Online:2022-08-25 Published:2022-08-02
• Supported by:
This research was supported by the National Natural Science Foundation of China under Grant Nos. 61973014 and 61573044

TIE Lin. Positive-Controllability, Positive-Near-Controllability, and Canonical Forms of Driftless Discrete-Time Bilinear Systems[J]. Journal of Systems Science and Complexity, 2022, 35(4): 1225-1243.

Controllable canonical forms play important roles in the analysis and design of control systems. In this paper, a fundamental class of discrete-time bilinear systems are considered. Such systems are of interest since, on one hand, they have the most complete controllability theory. On the other hand, they can be nearly-controllable even if controllability fails. Firstly, controllability of the systems with positive control inputs is studied and necessary and sufficient algebraic criteria for positive-controllability and positive-near-controllability are derived. Then, controllable canonical forms and nearly-controllable canonical forms of the systems are presented, respectively, where the corresponding transformation matrices are also explicitly constructed. Examples are given to demonstrate the effectiveness of the derived controllability criteria and controllable canonical forms.
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