Stability Analysis Of Two Kinds Of PWM Feedback Systems

In natural science and engineering application, time delay is widely existed, itmakes most of dynamical systems unstable. How to eliminate this effect is becoming ahot issue in engineering control. When this issue is studied by mathematical method,abstraction is made, and the mathematical model of the systems is established.Especially, if we want to get a more effective result in research of the issue, time delaysshould be considered.PWM (pulse width modulation) technology is flexible to be controlled, so it iswidely applied in the field of system stability analysis. Therefore, more and morescholars devote themselves into the area of PWM feedback systems, and they haveestablished a set of mature theory systems. As the random disturbance and time delay inpractical application are existed and their impacts are huge, they should not be ignoredwhen the PWM feedback systems are researched.In this paper, the stability problems of PWM feedback system with time-varyingdelays and nonlinear PWM time-delayed system are systematically studied. Accordingto the characteristics of the systems, PWM is added. Then rational Lyapunov-Krasovskiifunctional is chosen and constructed. Last, with the help of LMI (linear matrixinequality), criteria of p-th moment exponential stability and p-th moment exponentialasymptotic stability of two kinds of systems are given, which are effective and lessconservative. The main researches of this manuscript are as follows,1. Based on the theoretical achievements of predecessors, PWM is added into thesystems, which is applicable in engineering control. Conclusions of stochasticdynamical systems are generalized to the stochastic PWM feedback system andnonlinear PWM feedback system.2. Stochastic disturbance and time delays are sufficient considered. Inmathematical model of two kinds of systems in part3and part4, certain time delay andstochastic disturbance which satisfies the Wiener process (Brownian movement) areadded.3. In research of stochastic feedback system in this paper, we get a system modelthrough variable substitution. Then, we choose and construct an appropriate Lyapunov-Krasovskii functional. With the help of LMI, criteria of p-th momentexponential stability and p-th moment exponential asymptotic stability of the stochasticPWM feedback system with time-varying delays are obtained.4. In research of nonlinear time-delayed system in this paper, we make a systemtransformation by introducing new variables. Then, we choose and construct animproved functional. With the help of LMI, criteria of p-th moment exponential stabilityand p-th moment exponential asymptotic stability of nonlinear PWM time-delayedsystem we can get.