This paper considers the problem of output feedback control for non-square multi-input multi-output systems with arbitrary relative degree. The proposed controller, based on the L1 adaptive control architecture, is designed using the right interactor matrix and a suitably defined projection matrix. A state-output predictor, a low-pass filter, and adaptive laws are introduced that achieve output tracking of a desired reference signal. It is shown that the proposed control strategy guarantees closed-loop stability with arbitrarily small steady-state errors. The transient performance in the presence of non-zero initialization errors is quantified in terms of decreasing functions. Rigorous mathematical analysis and illustrative examples are provided to validate the theoretical claims.

中文翻译：

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具有任意相对度的非平方系统的 L1 自适应输出反馈

本文考虑了具有任意相对度的非方形多输入多输出系统的输出反馈控制问题。所提出的控制器基于 L1 自适应控制架构，使用正确的交互器矩阵和适当定义的投影矩阵进行设计。引入了状态输出预测器、低通滤波器和自适应律，以实现所需参考信号的输出跟踪。结果表明，所提出的控制策略保证了具有任意小的稳态误差的闭环稳定性。存在非零初始化错误时的瞬态性能根据递减函数进行量化。提供了严格的数学分析和说明性示例以验证理论主张。