分数阶线性系统的能观性研究

Research on observability of the fractional-order linear systems

在对一类由分数阶线性微分方程描述的系统的能观性问题研究中,通过分数阶线性定常系统求解,给出了分数阶线性定常和时变系统一般解的统一表达式。在给出分数阶系统能观性定义的基础上,提出并证明了分数阶线性系统时变和定常系统能观性的充分和必要条件,以及分数阶线性定常系统的能观性判据,所得结论对分数阶控制系统的分析与综合是有益的。

The observability for the systems described by a class of fractional-order linear differential equations is mainly investigated. The generalization of the usual complete solution formulae of the fractional-order linear system are derived not only for time-invariant case but also for time-varying case. The observability's definition of fractional-order linear systems is presented. The sufficient and necessary conditions for state observability of such systems are established and the corresponding criteria for fractional-order time-invariant systems are also obtained. The conclusion drawn is helpful to the analysis and synthesis of the fractional-lorder control system.