Indices of equilibrium points of linear control systems with saturated state feedback

TL;DR

This paper studies equilibrium points in n-dimensional linear control systems with saturated feedback, providing an index formula and exploring their relation to attraction basins and convexity.

Contribution

It introduces a new index formula for equilibrium points and analyzes their relation to attraction basin boundaries and convexity in saturated feedback systems.

Findings

Derived an index formula for equilibrium points.

Linked equilibrium point indices to attraction basin boundaries.

Discussed convexity properties of attraction basins.

Abstract

In this paper we investigate some properties of equilibrium points in n-dimensional linear control systems with saturated state feedback. We provide an index formula for equilibrium points and discuss its relation to boundaries of attraction basins in feedback systems with single input. In addition, we also touch upon convexity of attraction basin.