Controller Design And Stability Analysis Of Random-order Nonlinear Systems

When global stabilizable controllers for stochastic nonlinear systems are designed by using Lyapunov stability theory, even for a simple linear time-invariant system, its closed-loop system can usually be transformed into the highly nonlinear equation. The input-output signals given by the closed-loop system are usually complex stochastic process, so "nonlinear" and "stochastic" are the main difficulty for control theory investigation. Because of this essential reason, many typical and basic problems of control theory aren't been solved for a long time. This paper will focus on the study of the problems of state-feedback and output-feedback stabilization for stochastic high-order nonlinear systems.The main contributions include:1. The second chapter investigates the problem of globally asymptotically stable in prob-ability by state-feedback for a class of stochastic high-order nonlinear systems with a ratio of odd integers power. By extending the adding a power integrator technique and choosing an appropriate Lyapunov function, a linear smooth state-feedback controller is explicitly constructed to render the system globally asymptotically stable in probability. Furthermore, we address the problem of state-feedback inverse optimal stabilization in probability.2. The third chapter investigates the problem of output-feedback control for a class of stochastic high-order nonlinear systems with a ratio of odd integers power. By extending the adding a power integrator technique, introducing a new rescaling transformation, and choosing an appropriate Lyapunov function, an output-feedback controller is constructed to render the closed-loop system globally asymptotically stable in probability and the output can be regulated to the origin almost surely. Furthermore, we address the problem of inverse optimal stabilization in probability.