四阶时变离散系统的一致渐近稳定性

特征建模的方法为智能控制器设计和一些高阶对象进行低阶控制器设计提供了理论依据．对于速度跟踪、加速度控制,基于特征模型设计的自适应控制方案其稳定性问题即为四阶时变离散系统的稳定性问题．首先给出了变系数二次三项式的系数满足一组较复杂的差分关系式时,其判别式的简洁表达式,在此基础上,利用Lyapunov直接方法定量地给出了四阶线性时变离散系统的一致渐近稳定性判据．获得的结果仅依赖于系统方程系数变化范围,从而简化了现有的依赖于系统方程系数函数变化范围的结论．

Uniformly asymptotic stability of the 4th-order time-varying discrete systems

The principle of characteristic modelling provides a theoretical basis for the design of intelligent controllers and the control of higher-order plants by using lower controllers.For the control of speed tracking or acceleration,the sta- bility of the adaptive control systems based on characteristic modelling is exactly the stability of the 4th-order time-varying discrete systems.The brief expressions of discriminants for the varying coefficient quadratic trinomials are deduced when their coefficients satisfy complicated system of difference equations.Based on the results,the uniformly asymptotic stabil- ity criteria of the 4th-order linear time-varying discrete systems are also quantitatively given by employing the Lyapunov's direct method.The obtained results are only related to the variation ranges of coefficients in the system equation,thus simplifying the existing results in their dependence on the variation ranges of some coefficient functions.