Robust DR-admissibility of uncertain descriptor systems via LMI approach

This paper deals with the robust DR-admissibility of descriptor systems. The research for robustness bounds for descriptor systems is addressed. The use of parameter-dependent Lyapunov functions allows ones to handle uncertain singular systems whose uncertainty is polytopic norm-bounded (i.e. the state matrix can be written A+J∆L where A, J and L belong to a polytope of matrices and ∆ is unknown). If the 2-norm of ∆ is less than a robustness bound to be determined, the eigenvalues of any pencil (E,A + J∆L) in the uncertainty domain are clustered in an Ellipsoidal Matrix Inequality (EMI)-region. The proposed bound is easy to compute by using LMI tools.