Computation of controllability and observability Gramians in modeling of discrete‐time noncommensurate fractional‐order systems

Abstract

This paper presents a new algorithm for computation of controllability and observability Gramians for an expanded state space form of integer-order approximator to linear time-invariant discrete-time noncommensurate fractional-order systems. The introduced methodology can significantly reduce the time complexity of the Gramians' calculation, being the main computational burden in modeling of discrete-time fractional-order systems by means of a high integer-order expanded state space approximator and the balanced truncation reduction method. Simulation experiments illustrate an efficiency of the introduced methodology, in particular for low-dimension fractional-order systems and high implementation lengths.

Approximate controllability of higher order Riemann–Liouville fractional systems via cosine family

“…In last two decades, the existence and controllability results for the differential equations involving Caputo derivatives have been presented in many papers (see [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] and references therein). However, only few articles are reported on the controllability of Riemann-Liouville fractional differential equations.…”

Existence and controllability of second‐order nonlinear retarded integro‐differential systems with multiple delays in control

“…The controllability concept has become an active area of research due to its huge applications in the field of physics. There are many articles on controllability of systems represented by differential inclusions and differential equations (see [3][4][5][6][7][8][9][10][11][12][13][14][15][16] and references therein). Among them, controllability property for linear differential systems involving variable delay was discussed in [5].…”

Discrete‐time fractional fuzzy control of electrically driven mechanical systems

“…Fractional-order operators constitute promising tools for modeling and control of advanced and complex phenomena [41][42][43][44] since these operators consider and modulate a wider variety of memory properties. Fractional operators have been extended to the discrete-time case, with the purpose of obtaining more precise models and more flexible control structures [45,46].…”