Robust delay-dependent stability and stabilization of polytopic systems with time-delay and its application to flight control

Abstract

This paper concerns the problem of robust stability analysis and control synthesis for a polytopic system with time-varying delays via parameter-dependent Lyapunov functions. By a relaxation approach with slack matrices and a descriptor model transformation, a new robust delay dependent stability criterion is expressed as a set of linear matrix inequalities (LMIs) with less computational burden. This criterion can be employed for robust controller synthesis. The obtained stabilizability criterion is applied to design a flight controller for aircraft dynamic systems with multiple operating points. The simulation results illustrate the effectiveness of the proposed approach.