Prescribed Performance Control of Two-Time-Scale Systems and Its Application

Abstract

This article explores the prescribed performance control design for linear two-time-scale systems (TTSSs). Due to ill-conditioning and high dimensionality, existing prescribed performance control methods for single-time-scale systems are unsuitable for TTSSs. Moreover, current TTSS methodologies focus on steady-state performance, often neglecting transient dynamics. To address these challenges, we first apply the Chang transformation to decouple the fast and slow states. Next, we use a state transformation to convert the state equation into block form to eliminate the requirement of a full row-rank input matrix. Finally, the backstepping method is utilized to design the prescribed performance control. The effectiveness and advantages of the proposed control strategy are demonstrated through two examples: a numerical simulation and a hardware-in-the-loop experiment involving an electronic circuit system.