TY - CHAP
T1 - Controllability and Stability of Semilinear Fractional Order Systems
AU - Klamka, Jerzy
AU - Babiarz, Artur
AU - Czornik, Adam
AU - Niezabitowski, Michał
N1 - Publisher Copyright:
© 2021, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG.
PY - 2021
Y1 - 2021
N2 - In the chapter two the most important properties of fractional order dynamical systems, namely, controllability and stability are presented. At the beginning the basic notations and the fundamental definitions are recalled. The first part of the chapter is devoted to controllability and contains the formulation of the problem, main hypotheses and theorems about controllability of semilinear fractional order systems with distributed and point multiplicities constant or variable delays in the state variables and controls. Next, using fixed point theorems approximate controllability problem in infinite dimensional spaces, in particular Banach or Hilbert space, are discussed. Second part of the chapter is devoted to the stability problem of fractional order systems. The problem of stability and the problem of the existence of solutions for linear and nonlinear fractional order systems are also presented.
AB - In the chapter two the most important properties of fractional order dynamical systems, namely, controllability and stability are presented. At the beginning the basic notations and the fundamental definitions are recalled. The first part of the chapter is devoted to controllability and contains the formulation of the problem, main hypotheses and theorems about controllability of semilinear fractional order systems with distributed and point multiplicities constant or variable delays in the state variables and controls. Next, using fixed point theorems approximate controllability problem in infinite dimensional spaces, in particular Banach or Hilbert space, are discussed. Second part of the chapter is devoted to the stability problem of fractional order systems. The problem of stability and the problem of the existence of solutions for linear and nonlinear fractional order systems are also presented.
UR - https://www.scopus.com/pages/publications/85091101497
U2 - 10.1007/978-3-030-48587-0_9
DO - 10.1007/978-3-030-48587-0_9
M3 - Chapter
AN - SCOPUS:85091101497
T3 - Studies in Systems, Decision and Control
SP - 267
EP - 290
BT - Studies in Systems, Decision and Control
PB - Springer Science and Business Media Deutschland GmbH
ER -