Necessary and sufficient stability criteria for linear systems with delays

Abstract

New necessary and sufficient stability criteria for linear systems with multiple uncertain delays are established by using the time-domain and the frequency-domain methods, respectively. The results are first established based on a new-type time-domain stability theorem for retarded dynamical systems and a new technique for estimating the derivative of Lyapunov function along the solution of system at some specific instants. Then, the same criteria are derived by the frequency-domain techniques. The established stability criteria are not only the least conservative but also involve the least tuning parameters.