H∞ Control with Transients for Singular Systems

In this paper, the problem of a generalized type of H∞ control is investigated for continuous-time singular systems, which treats a mixed attenuation of exogenous inputs and initial conditions. First, a performance measure that is essentially the worst-case norm of the regulated outputs over all exogenous inputs and initial conditions is introduced. A necessary and sufficient condition is obtained to ensure the singular system to be admissible and the performance measure to be less than a prescribed scalar. Based on the criterion a sufficient condition for the existence of a state-feedback controller is established in terms of linear matrix inequalities. Moreover, the relationship between the performance measure and the standard H∞ norm of the system is provided. Two numerical examples are given to demonstrate the properties of the obtained results.

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