Feedback control for damping a system of linear oscillators

TL;DR

This paper presents a unified feedback control strategy for damping multiple linear oscillators, combining high-energy asymptotic theory and Lyapunov methods for effective stabilization.

Contribution

It introduces a novel bounded feedback control design applicable to any number of oscillators, integrating asymptotic and Lyapunov approaches for improved damping.

Findings

Effective damping achieved for systems with multiple oscillators

Control adapts with energy levels to maintain boundedness

Special cases for one and two oscillators are analyzed

Abstract

The paper is devoted to a design of a common bounded feedback control steering a system of an arbitrary number of linear oscillators to the equilibrium. At high energies, the control is based on the asymptotic theory of reachable sets of linear systems. With decreasing of the energy, a similar control with a reduced upper bound is used. On the final stage, the control is constructed by using the method of common Lyapunov functions. Special attention is paid to the cases of one and two oscillators.