关于Caputo分数阶微分系统的能控性和能观性的Chebyshev系统和非均匀采样
On Chebyshev systems and non-uniform sampling related to controllability and observability of caputo fractional differential systems
摘要：
研究了任意实α阶Caputo分数阶线性线性系的能控性和能观性。首先得到了演化算子的动力学矩阵幂展开式的表达式。线性无关的连续函数或矩阵函数的集合，也是切比雪夫系统，以自然的方式出现在这样的展开式中。基于这类函数的性质，讨论了α = 1的Caputo分数阶微分系统的能控性和能观性与相应标准系统的能控性和能观性的关系.在非均匀抽样条件下，对这些性质的满足进行了推广.证明了在选择合适的采样时刻时，并不受相关Chebyshev系统性质的限制
英文摘要：
This paper is concerned with the investigation of the controllability and observability of Caputo fractional differential linear systems of any real order α . Expressions for the expansions of the evolution operators in powers of the matrix of dynamics are first obtained. Sets of linearly independent continuous functions or matrix functions, which are also Chebyshev systems, appear in such expansions in a natural way. Based on the properties of such functions, the controllability and observability of the Caputo fractional differential system of real order α are discussed as related to their counterpart properties in the corresponding standard system defined for α = 1. Extensions are given to the fulfilment of those properties under non- uniform sampling. It is proved that the choice of the appropriate sampling instants ion not restrictive as a result of the properties of the associate Chebyshev systems
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