Controllability, reachability and minimum energy control of fractional discrete-time linear systems with multiple delays in state

Abstract

Abstract. In the paper the problems of controllability, reachability and minimum energy control of a fractional discrete-time linear system with delays in state are addressed. A general form of solution of the state equation of the system is given and necessary and sufficient conditions for controllability, reachability and minimum energy control are established. The problems are considered for systems with unbounded and bounded inputs. The considerations are illustrated by numerical examples. Influence of a value of the fractional order on an optimal value of the performance index of the minimum energy control is examined on an example.

Minimum Energy Control of Fractional Descriptor Discrete‐Time Linear Systems with Bounded Inputs Using The DRAZIN Inverse

“…Some recent interesting results in fractional systems theory and its applications can be found in . Minimum energy control of fractional systems has been addressed in .…”

“…The Drazin inverse for solving the state equation of fractional continuous‐time linear systems has been applied in and the controllability, reachability, and minimum energy control of fractional discrete‐time linear systems with delays in state have been investigated in . A comparison of three different methods for solving the descriptor fractional discrete‐time linear system has been made in .…”

Higher order fuzzy logic in controlling selective catalytic reduction systems

“…Examples of fuzzy logic systems applications are broadly known, e.g. [3][4][5]. Another work on FLSs in the industry and the environment is [6].…”

Reachability of fractional dynamical systems using ψ-Hilfer pseudo-fractional derivative

“…Kociszewski [28] proposed the reachability of fractional discrete-time linear systems with delays in state and control. Similarly, reachability for the fractional discrete-time linear systems with multiple delays in state was investigated by Buslowicz in [9].…”