Mixed $L_1/H_\infty$-synthesis for $L_\infty$-stability

TL;DR

This paper introduces a novel mixed $L_1/H_ _ ext{infty}$-synthesis method for stabilizing non-linear systems with sector constraints, optimizing peak-to-peak norms under $H_ ext{infty}$ constraints, ensuring local exponential stability and global BIBO stability.

Contribution

The paper presents a new synthesis approach combining $L_1$ and $H_ ext{infty}$ methods for non-linear control systems with sector constraints, enhancing stability and performance.

Findings

Successfully stabilizes non-linear systems with sector constraints

Achieves local exponential stability and global BIBO stability

Optimizes closed-loop peak-to-peak system norm

Abstract

We consider stabilization and performance optimization of non-linear controlled systems, where the non-linearity satisfies a sector constraint asymptotically. This leads to optimization of the closed loop peak-to-peak system norm subject to $H_\infty$-performance constraints. Non-linear controlled systems tuned successfully by this novel approach are locally exponentially stable and globally BIBO-stable.