A Small-Gain Theorem with Applications to Input/Output Systems, Incremental Stability, Detectability, and Interconnections

A rolled-off passivity theorem

Given two nonlinear systems which only violate incremental passivity when their incremental gains are sufficiently small, we give a condition for their negative feedback interconnection to have finite incremental gain, which generalizes the incremental small gain and incremental passivity theorems. The property may be determined graphically by plotting the Scaled Relative Graphs (SRGs) of the systems, which provides engineering significance to the mathematical result.

SISO非线性系统一般互连的缩放相对图分析

Scaled Relative Graph Analysis of General Interconnections of SISO Nonlinear Systems

本文针对缩放相对图分析非线性系统的适用性缺陷，提出将SRG重构并与Nyquist判据结合的新方法，给出一般互连稳定性与$L_2$增益判据，并推广圆判据以处理更广泛非线性。

神经网络反馈系统的可扩展增量鲁棒性分析

Scalable Incremental Robustness Analysis of Neural Network Feedback Systems

本文提出统一可扩展框架，结合SDP分解与Lipschitz估计，实现大规模神经网络反馈系统的增量鲁棒性分析，获得与深度无关的LMI条件及最先进的增益界。

软和硬缩放相对图用于非线性反馈稳定性

Soft and Hard Scaled Relative Graphs for Nonlinear Feedback Stability

本文基于软和硬缩放相对图分析非线性反馈系统的输入-输出稳定性，通过区分增量正性和增量被动性，提出无需弦假设的稳定性判定方法，适用于有界和无界的开环系统。

Non-Euclidean Contraction Theory for Robust Nonlinear Stability

We study necessary and sufficient conditions for contraction and incremental stability of dynamical systems with respect to non-Euclidean norms. First, we introduce weak pairings as a framework to study contractivity with respect to arbitrary norms, and characterize their properties. We introduce and study the sign and max pairings for the $\ell_1$ and $\ell_\infty$ norms, respectively. Using weak pairings, we establish five equivalent characterizations for contraction, including the one-sided Lipschitz condition for the vector field as well as matrix measure and Demidovich conditions for the …

Constrained nonlinear output regulation using model predictive control -- extended version

We present a model predictive control (MPC) framework to solve the constrained nonlinear output regulation problem. The main feature of the proposed framework is that the application does not require the solution to classical regulator (Francis-Byrnes-Isidori) equations or any other offline design procedure. In particular, the proposed formulation simply minimizes the predicted output error, possibly with some input regularization. Instead of using terminal cost/sets or a positive definite stage cost as is standard in MPC theory, we build on the theoretical results by Grimm et al. 2005 using a…