L2 Gain Stability of Switched Output Feedback Controllers for a Class of LTI Systems

Abstract—Our previous work has been devoted to designing asymptotically stabilizing switching controllers for a class of second order LTI plants. Here, we extend the results of our pre-vious work by proving that, when a plant can be asymptotically stabilized using a particular switching architecture, the overall closed-loop interconnection is also finite L2 gain stable. We shall first prove this result for a simplified problem in which a portion of the switching architecture has full access to the state of the plant and shall then extend to the case where the architecture only has access to the plant output by designing an appropriate observer. Index Terms—Controller design, hybrid systems, L2 gain, output feedback, switching systems