Reduced-Order $H_{\infty}$ Filter and Controller Co-Design for Switched Uncertain Systems: An Output Feedback Method

It is addressed the reduced-order $H_{\infty}$ filter and controller co-design for switched uncertain systems via an output feedback method in the paper. By reformulating the coefficient matrices, the generalized $H_{\infty}$ filtering control issue for switched uncertain systems can be transformed into an output feedback control problem for a class of switched uncertain systems. This transformation allows for seeking out an output feedback control law, providing two sufficient conditions in the form of linear matrix inequalities (LMIs) to ensure exponential stability with a weighted $H_{\infty}$ performance for the generalized closed-loop system. Furthermore, the proposed method enables the realization of the co-design of reduced-order $H_{\infty}$ filter and controller in two distinct forms, which are compared through numerical examples to highlight their effectiveness. The novelty of this method lies in its ability to handle both reduced-order $H_{\infty}$ filtering and control design simultaneously through a unified framework and improving flexibility.