The problem of guaranteeing stability from the entire null controllable region (NCR) for multi-input linear dynamical systems is addressed in the present manuscript. The proposed controller design is inspired by results for single input systems and generalized to multiple input systems. The approach relies on utilizing the level sets of the NCR as level sets of a Lyapunov function. A contractive constraint is incorporated into a model predictive control design, guaranteeing feasibility for any horizon length, and resulting in the NCR as the closed-loop stability region. The proposed method is illustrated using a simulation example.

中文翻译：

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零可控区域在多输入线性系统模型预测控制中的定义与应用

在本手稿中解决了为多输入线性动力学系统从整个零可控区域（NCR）保证稳定性的问题。所提出的控制器设计受到单个输入系统结果的启发，并被推广到多个输入系统。该方法依赖于将NCR的级别集用作Lyapunov函数的级别集。收缩约束被合并到模型预测控制设计中，从而保证了任何视界长度的可行性，并导致NCR作为闭环稳定区域。通过仿真示例说明了所提出的方法。