Lyapunov Stabilization of Large‐Scale Continuous Systems Based on the Dissipativity Method and Output Feedback Control

ABSTRACT This paper investigates the exponential stabilization of large‐scale continuous dynamical systems (LSCDS) through the application of linear static output feedback (SOF). Initially, a linear SOF controller is developed to facilitate the stabilization of LSCDS. By employing the concept of vector dissipativity, a necessary and sufficient criterion is formulated to guarantee the system's exponential stabilization. Furthermore, stability analysis is conducted using linear matrix inequality (LMI) conditions, which serve as the foundation for determining the system's asymptotic behavior under SOF control. Leveraging vector dissipativity, an alternative necessary and sufficient condition is introduced for stabilizing LSCDS. Lastly, examples are presented to demonstrate the validity and practical applicability of the proposed findings.