Stability Analysis For A Class Of Affine Nonlinear Control Systems Based On Differential Lyapunov Framework

Differential geometry control method is widely applied in nonlinear controlsystem. It has become a powerful tool to analyse and discuss the stability,tracking,synchronization etc. for nonlinear control systems. Differential passive control systemconnects differential storage functions and differential Lyapunov functions. It studiesthe solutions, properties of systems such as tracking, synchronization and so on, byjudging the distance between the solutions of the system. In this paper, based on theframework of differential Lyapunov, we studied the differential passive property ofaffine nonlinear control system, and got the incremental stability by using differentialpassivity.First of all, based on the differential Lyapunov framework，we discussed thedifferential passivity for one class of cascade systems. Many nonlinear controlsystems can be converted to cascade systems by state feedback or controller design.At the same time, cascade system also represents a class of practical systems. we alsostudied the relationship between differential passivity and incremental stability ofcascade system by differential storage functions and differential Lyapunov functions.Then we discussed the incremental stability of this kind of cascade system.Secondly, we studied the differential passivity of three-phase voltage type PWMrectifier. The three-phase voltage type PWM rectifier has many advantages. It realizesthe green transformation of electrical energy. Various of nonlinear control theorieshave been applied into rectifier control. In this paper, according to EL mathematicalmodel for PWM rectifier. We designed the differential passive controller for thesystem, which made the rectifier reach an ideal stable state quickly by usingdifferential Lyapunov method.