发表机构
Eindhoven University of Technology; Université catholique de Louvain（埃因霍温理工大学; 天主教鲁汶大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对离散时间投影控制系统，提出基于投影度量保持二次增量稳定性和小增益条件，以及直接李雅普诺夫方法，实现增量稳定性与收敛性分析，并通过示例和非线性Bode图验证。
AI 中文摘要
基于投影的控制器可以通过投影修改控制器的输入-输出行为，从而克服经典线性时不变控制的基本限制。一个关键例子是混合积分器-增益系统，即一种投影积分器，最近已在多个工业系统中得到成功应用。虽然先前关于基于投影的控制系统的分析与设计工作主要集中于连续时间设置和非增量分析，但需要更精细的离散时间增量分析，以更好地反映实际数字实现并获得更准确的（鲁棒）性能评估。为满足这一需求，本文研究了离散时间基于投影的控制系统的增量稳定性与收敛性分析。我们的第一种方法基于证明：如果投影度量设计得当，此类控制器能保持其标称（未投影）动态的二次增量稳定性。在此基础上，我们推导出一个小增益条件，保证投影控制器与一般非线性被控对象互联时的增量输入-状态稳定性。第二种方法基于直接的李雅普诺夫方法，用于验证输入仿射分段光滑系统中的增量稳定性，这可视为经典离散时间Demidovic条件的扩展。我们通过多个示例说明我们的结果，并通过非线性Bode图展示性能量化，特别关注一阶投影元件。
英文摘要
Projection-based controllers can overcome fundamental limitations of classical linear time-invariant control by modifying the controller's input-output behavior via projection. A key example is given by the hybrid integrator-gain system, a projected integrator, which has recently found successful application in several industrial systems. While prior work on analysis and design of projection-based control systems has primarily focused on the continuous-time setting and non-incremental analysis, a more refined incremental analysis in discrete-time is needed to better reflect actual digital implementation and obtain more accurate (robust) performance assessment. To address this need, this paper considers incremental stability and convergence analysis of discrete-time projection-based control systems. Our first methodology is based on showing that such controllers preserve the quadratic incremental stability of their nominal (unprojected) dynamics, if the projection metric is well-designed. Building on this, we derive a small-gain condition guaranteeing incremental input-to-state stability for interconnections of projected controllers with general nonlinear plants. A second approach is grounded in a direct Lyapunov-based method for verifying incremental stability in input-affine piecewise-smooth systems, which can be seen as an extension of the classical discrete-time Demidovic conditions. We illustrate our results through several examples, and demonstrate performance quantification via nonlinear Bode plots, with a special focus on first-order projection elements.
DOI：10.1016/j.nahs.2026.101813
