ABSTRACT

Sufficient conditions for the exponential stability and stabilisability of linear singularly perturbed control systems with the small parameter defined on homogeneous time scale are studied. Stability conditions are formulated in terms of a spectrum of two parameter-free subsystems of lower dimensions than the original one: slow and fast subsystems. These conditions, being parameter-free, provide the exponential stability of the original singularly perturbed system with delay for all sufficiently small positive values of parameter, i.e. robust with respect to the parameter of singular perturbation. A stabilisation problem for a given class of control systems is solved by a design of a linear well-conditioned parameter-free composite state-feedback control which is a sum of a stabilising slow and fast control.

摘要

研究了齐次时间尺度上定义的小参数线性奇异摄动控制系统的指数稳定性和稳定性的充分条件。稳定性条件是根据比原始子系统低维的两个无参数子系统的频谱来表示的：慢子系统和快速子系统。这些条件，是无参数的，提供了原始奇异摄动系统的指数稳定性，对于所有足够小的正参数值都有延迟，即相对于奇异摄动的参数是稳健的。给定类别的控制系统的稳定问题通过设计线性条件良好的无参数复合状态反馈控制来解决，该控制是稳定慢速和快速控制的总和。