Dissipative analysis and control of time-varying singular systems with symmetries

This paper delves into the design and analysis of output feedback controllers for dissipative linear time-varying singular systems that exhibit state-space symmetry. We detail the development of both static and dynamic symmetrical output feedback controllers, highlighting their design processes and the necessary and sufficient conditions for achieving strict dissipation. Special attention is given to the symmetry conditions that govern the effectiveness of these controllers. Additionally, we establish the criteria for system admissibility and dissipation through matrix inequalities, supported by rigorous theoretical proofs. The practical applicability of our theoretical findings is demonstrated through the implementation and testing of the controllers in simulated environments, ensuring their performance under various operational conditions. Our results indicate that the designed controllers effectively maintain the desired system properties, contributing to the stability and robust performance of time-varying singular systems.