A Class Of Generalized Neutral System Stability And Robust Control Research

Since time delay is frequently a source of instability and poor performance, the stability analysis of delay-differential systems has been widely investigated in the last decades. Recently, the stability analysis of the delay systems of neutral type has been studied by some researchers. Singular system of neutral type is more widely, so it has profound theory significance and practical value to investigate the stability analysis and synthesis problem of the time-delay general systems of neutral type.This paper studied the stability and control problems of the singular systems of neutral type by using Lyapunov method and state solution approach, constructing Lyapunov functional, using linear matrix inequality, some stability criteria and H_∞controller and observer-based controller of the neutral time-delay general systems were given.First, the stability of the singular neutral systems with single time-delays, mixed time-delays, distributed delays, and nonlinear perturbations were studied. Based on Lyapunov method, the system asymptotic stability criteria were given in terms of linear matrix inequalities. The corresponding robust H_∞controller designing methods were given in the terms of linear matrix inequalities. Second, the asymptotic stability of the neutral singular systems with time-varying delays was taken into account. Asymptotic stability criterions of neutral general systems with discrete and distributed delays were given. Finally, the stabilization problem and observer-based control of linear time-delay singular neutral systems with single delay were investigated. By using LMI approach, we provided a criterion to design the observer gain and the controller gain simultaneously. Some examples and computer simulation results were provided to illustrate our main results.