The positive (minimal) realization problem for a class of singular discrete-time linear single-input, single-output systems with delays in state and delays in control is addressed. Solvability conditions for the positive (minimal) realization problem are established. It is shown that there exists a positive (minimal) realization of an improper transfer function T(z) = n(z) / d(z) if the coefficients of polynomial n(z) are non-negative and of the polynomial d(z) are non-positive except the leading one, which should be positive. A procedure for computation of the positive (minimal) realization of the transfer function is proposed and illustrated by an example.
This paper presents a position sensorless drive of non salient pole PM synchronous motors for all speeds including zero speed. Using adaptive Lyapunov design a new approach for the design of an observer is developed. The resulting scheme leads to a nonlinear full order observer for the motor states including the rotor speed. Assuming motor parameters known the design achieves stability with guaranteed region of attraction even at zero speed. The control method is made robust at zero and low speed by changing the direct vector current component to a value different from zero. In order to verify the applicability of the method the controller has been implemented and tested on a 800 W motor.