Asymptotical stabilization of the nonlinear upper triangular fractional-order systems

Abstract

This paper introduces a simple method of the design of the output feedback stabilizing controller (OFSC) for the nonlinear upper triangular fractional-order systems (NUTFOS). The OFSC which makes the closed-loop system asymptotically stable is given based on the fractional indirect Lyapunov method and the static gain control method. Furthermore, an algorithm is established to design OFSC for the NUTFOS. Finally, an example is presented to verify the validity of the proposed method.

Stability Results for a Coupled System of Impulsive Fractional Differential Equations

“…Definition 5. [61] Problem (1) is generalized Ulam-Hyers stable if there exists a function Θ α,β ∈ C(R + , R + ), Θ α,β (0) = 0 for each > 0, such that for every solution (x, y) ∈ Y of the inequality (28). there is a solution (ζ, χ) ∈ Y of (1) such that (x, y)(t) − (ζ, χ)(t) Θ α,β ( ).…”

“…Proof. Let (x, y) ∈ Y be any solution of the inequality (28) and let (ζ, χ) ∈ Y be the unique solution of the following:…”

“…On the other hand, it is impossible to describe the complicated systems and processes with a single differential equation. Therefore, the coupled systems involving FDEs have also received incredible attention; consequently, many results are devoted to them [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31].…”

Positive Solutions for a System of Hadamard-Type Fractional Differential Equations with Semipositone Nonlinearities

“…Coupled systems of fractional-order differential equations have also been investigated by many authors (see [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][25][26][27][28][29][30][31][32][33][34][35][36] and the references therein). In [7], the authors used coincidence degree theory to establish an existence result for a coupled system of nonlinear fractional differential equations:…”