Robust stability analysis of fractional-order uncertain singular nonlinear system with external disturbance

New Results on Stabilization of Fractional‐Order Nonlinear Systems via an LMI Approach

“…Moreover, many systems modelled with the help of fractional calculus display rich fractional dynamical behavior, such as viscoelastic systems [10], boundary layer effects in ducts [11], electromagnetic waves [12], fractional kinetics [13,14], and electrode-electrolyte polarization [15,16]. Many stability conditions have been proposed for linear fractional-order systems [17][18][19][20][21][22][23], fractional-order nonlinear systems [24][25][26][27][28][29][30], fractional-order neural networks [31,32], fractional-order switched linear systems [33,34], fractional-order singular systems [35,36], positive fractional-order systems [37,38] and fractional chaotic complex networks systems [39]. Many stability conditions have been proposed for linear fractional-order systems [17][18][19][20][21][22][23], fractional-order nonlinear systems [24][25][26][27][28][29][30], fractional-order neural ne...…”

“…As a result, the problem of stability analysis and control of fractional-order systems is an important problem in the theory and applications of fractional calculus. Many stability conditions have been proposed for linear fractional-order systems [17][18][19][20][21][22][23], fractional-order nonlinear systems [24][25][26][27][28][29][30], fractional-order neural networks [31,32], fractional-order switched linear systems [33,34], fractional-order singular systems [35,36], positive fractional-order systems [37,38] and fractional chaotic complex networks systems [39]. Among the reported methods, the Lyapunov direct method provides an effective approach to analyze the stability of fractional nonlinear systems.…”

Robust Linear Neural Network for Constrained Quadratic Optimization

“…From Section 2.1, it follows that the equilibrium point's exponential stability of system (2) is equivalent to the exponential stability of the trivial solution of system (11). Notice that system (11) is a linear system structure; thus the exponential stability of the trivial solution of system (11) is equivalent to Re( ) < 0, where is an arbitrary eigenvalue of matrix …”

“…In order to reduce the conservation of the criterion established in [30], literature [31] further gave out an improved stable result as ‖ − ‖ 2 < 1. If we construct model (11) to solve problem (1), by direct computation, it follows that ‖ − ‖ 2 = 0.9984 < 1; from Theorem 8, it yields that the state vector of system (11) is exponentially convergent to the optimization value of problem (1). Simulation result is illustrated in Figure 1 with initial value [2, −1, 1.5] , from which one can see that the state vector of system (11) is convergent to the equilibrium point exponentially.…”

“…Mathematically, the optimization problem to be solved is mapped into a dynamical system so that its state output can give the optimal solution and the optimal solution is then obtained by tracking the state trajectory of the designed dynamical system based on the numerical ordinary differential equation technique [11]. From the pioneering work of McCulloch and Pittes, numerous neural network models have been developed.…”