Robust H2 control for descriptor system based on new bounded real lemma

This paper is concerned with the problem of robust H₂ control for uncertain continuous descriptor system based on new bounded real lemma. Our purpose is to present sufficient and necessary conditions such that the uncertain descriptor system is regular, impulse free and stable for all admissible uncertainties, while the H₂ norm of the descriptor system is less than a given positive number gamma. To this end, a new bounded real lemma for the robust H₂ control problem is firstly derived in terms of a strict linear matrix inequality (LMI). Secondly, based on this bounded real lemma, one method of designing a state feedback controller is developed to guarantee the robust H₂ performance. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.