Hybrid Output Feedback Stabilization for LTI Systems With Single Output

This note presents a hybrid control scheme for a class of continuous-time LTI systems that cannot be stabilized by a single static output feedback (SOF) controller. The main idea here is to design multiple SOF gains and proper logic rules that orchestrate switching among these gains so as to achieve the global stability. One challenge, however, is that the switching logic should be in the output feedback form as well. This may seriously restrict the possible choices of switching surfaces, especially when the output is just a scalar. To overcome this difficulty, a multirate sampling control scheme is proposed. Under this framework, a hybrid output feedback stabilizing controller is designed, and sufficient controller synthesis conditions are proposed as linear matrix inequalities based on multiple Lyapunov function theorems. The note concludes with a discussion on possible extensions and future research topics.