Extended H2, H∞ and pole placement LMI characterization for continuous-time systems

Abstract

In this paper, our goal is to extend the previously known results of the norm characterizations in the terms of the linear matrix inequalities. Our approach is based on a recently developed extended stability condition which contains as particular cases both the celebrated Lyapunov theorem for precisely known systems and the quadratic stability condition for uncertain continuous-time systems. It provides the opportunity to check stability using parameter-dependent Lyapunov functions which are derived from LMI conditions. In this paper, this feature is explored for deriving the extended analysis linear matrix inequalities of H2 -norm, Hinfin-norm and regional pole placement constraints. These extended norm characterization conditions exhibit a kind of decoupling between the Lyapunov and the system matrices, thus enable the checking of system performance using parameter-dependent Lyapunov matrices for uncertain continuous-time systems with convex polytopic uncertainty. Moreover, this feature provides a stepping stone for the design of controllers with multiobjective constraints as well as the design of robust H2 or Hinfin controllers without employing a unique Lyapunov matrix.