Controllability and stability of semilinear fractional order systems. (English) Zbl 1481.93013
Kulczycki, Piotr (ed.) et al., Automatic control, robotics, and information processing. Cham: Springer. Stud. Syst. Decis. Control 296, 267-290 (2021).
Summary: 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.
For the entire collection see [Zbl 1475.93005].
For the entire collection see [Zbl 1475.93005].
MSC:
93B05 | Controllability |
93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
93C10 | Nonlinear systems in control theory |
93C43 | Delay control/observation systems |
93C25 | Control/observation systems in abstract spaces |
26A33 | Fractional derivatives and integrals |