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H∞ performance analysis with transients for singular systems

In this paper, the problem of a generalized type of H∞ performance analysis 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. Necessary and sufficient conditions are obtained to ensure the singular system to be admissible and the performance measure to be less than a prescribed scalar. Moreover, the relationship between the performance measure and the standard H∞ norm of the system is provided. A numerical example is given to demonstrate the properties of the obtained results.