Control Design For Nonlinear Systems With Fraction Powers

In recent years, the fruitful theoretical and extensive practical applications in controller design and stability analysis for nonlinear systems with fraction powers have been achieved. For three classes of nonlinear systems with fraction powers in this dissertation, three state-feedback control approaches are presented. The main contributions include:1. The second chapter investigates the problem of state-feedback stabilization for a class of stochastic nonlinear time-delay systems with fraction powers. By extending the adding-a-power-integrator technique to the stochastic time-delay systems, a state-feedback controller is explicitly constructed such that the origin of closed-loop system is globally asymptotically stable in probability. The main design difficulty is to deal with the un-controllable linearization and the nonsmooth system perturbation, which, under some ap-propriate assumptions, can be solved by using the adding-a-power-integrator technique. Two simulation examples are given to illustrate the effectiveness of the control algorithm proposed in this chapter.2. The third chapter addresses the stabilization problem by state feedback for a class of nonlinear input-delay systems with fraction powers. The designed controller could achieve global asymptotical stability. Based on the appropriate state transformation of time-delay systems and the Lyapunov method, the problem of controller design can be convert into the problem of finding a parameter, which can be gotten by appraising the nonlinear terms of the systems. Finally, a simulation example is given to illustrate the effectiveness of the control algorithm proposed in this chapter.3. The fourth chapter states the problem of sampled-data control for a class of nonlin-ear systems with fraction powers. The controller design is based on the Euler approximation of the exact discretized model of the plant and the obtained control algorithm is novel. A state-feedback controller is constructed that guarantees a semiglobal practical asymptotic stability property for the closed-loop system. A simulation example is given to illustrate the effectiveness of the control algorithm proposed in this chapter.