LINEAR DISCRETE FRACTIONAL ORDER STATE-SPACE SYSTEM-PROPERTIES, ESTIMATION AND CONTROL

In recent years the concept of non-integer derivative and integral (fractional calculus) is used increasingly to model the behavior of real systems in various fields of science and engineering. This paper presents some basic results on the stability,controllability and observability of linear discrete fractional order state-space systems. The paper also presents a generalization of Kalman filter for linear discrete fractional order state-space systems. The discrete fractional system is first introduced. Then its properties is discussed, and the Kalman filter equations are derived. Finally, some numerical examples are presented