Observability for singular control systems of fractional order
Linear, finite-dimensional, continuous-time, singular control systems with constant coefficients and derivatives of fractional order are considered. Fundamental results from the theory of fractional order dynamical systems are recalled (see e.g. [\textit{K. S. Miller} and \textit{B. Ross}, ``An introduction to the fractional calculus and fractional differential equations'', John Wiley \& Sons, New York (1993)] for more details). Next, using algebraic methods, necessary and sufficient conditions for observability in a given finite-time interval are formulated and proved. A simple numerical example that illustrates the theoretical considerations is also given. Moreover, several remarks and comments concerning fractional order dynamical control systems are presented. Similar observability problems for fractional control systems have been recently considered in the paper [\textit{A. B. Shamardan} and \textit{M. R. A. Moubarak}, Controllability and observability for fractional control systems, J. Fractional Calc. 15, 25-34 (1999; Zbl 0964.93013)].
scientific article; zbMATH DE number 1626268