An algorithm is proposed for designing an input feedback matrix for rectangular descriptor systems, ensuring that the resulting closed-loop system has an index no greater than two and admits arbitrary initial conditions. A novel sufficient condition, expressed in terms of the system’s coefficient matrices, is established to achieve this goal. Moreover, if the system is impulse controllable, the same feedback matrix guarantees an impulse-free closed-loop response while still permitting arbitrary initial conditions. The effectiveness of the method is demonstrated through a constrained mechanical system and a supporting numerical example.
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