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.