Static Output Feedback Control for Linear Systems via Multiple Lyapunov Functions

This paper is concerned with the problem of synthesizing static output feedback (SOF) controllers for linear systems via multiple Lyapunov functions (LFs). By appending a zero block to the matrix related to the control input and incorporating a real matrix into the control gain accordingly, the closed-loop system is extended, thereby introducing additional degrees of freedom into the proposed synthesis conditions. Based on the proposed multiple LFs, which are constituted by the summation of LFs dependent on system states at different instants, sufficient conditions in terms of linear matrix inequalities (LMIs) are derived to ensure the stability and desired performance of the closed-loop system. Compared with the existing methods, the proposed scheme achieves decoupling without requiring the correlation matrix to possess a specific structure, and yields superior results. Finally, the effectiveness and superiority of the proposed technique are validated through simulation example.