Robust stability testing function and Kharitonov-like theorem for fractional order interval systems

Abstract

This study deals with the subject of robust bounded-input bounded-output (BIBO)-stability of a family of fractional order interval systems. Employing the idea of ‘robust stability testing function’ and extending it to the case of intended systems, a simple graphical procedure for checking the robust BIBO-stability applicable to both commensurate and incommensurate orders is developed. Moreover, a Kharitonov-like theorem is provided that presents necessary and sufficient conditions for checking the mentioned stability of the fractional order interval systems with commensurate order α belonging to [1,2), but only sufficient conditions for commensurate order α in interval (0,1). Besides, lower and upper bounds applicable to both commensurate and incommensurate cases are provided which are useful for simulation purposes. Finally, three numerical examples are given to illustrate the results.