State Feedback singular H ∞ Control for switched Linear Systems

This paper addresses the singular state feedback H∞ control for switched linear systems. The singular problem for switched linear systemS means that the gain matrix between the control input and the controlled output for each subsystem is not full column rank (FCR). First, the switched state feedback H∞ control problem is studied in the regular case. Then we show that, in the singular case, the singular H∞ control problem for the original switched linear system is equivalent to another H∞ control problem related to a reduced-order switched linear system. If this problem turns out to be regular, it can be solved. Conversely, we can iterate the reduction procedure. This iterative algorithm terminates when either a trivial problem is encountered or the last reduced-order problem is regular.

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