Fractional Differential Equations

In this paper, the problem of robust fault tolerant control for a class of singular systems subject to both time-varying state-dependent nonlinear perturbation and actuator saturation is investigated. A sufficient condition for the existence of a fixed-gain controller is first proposed which guarantees the regularity, impulse-free and stability of the closed-loop system under all possible faults. An optimization problem with LMI constraints is formulated to determine the largest contractively invariant ellipsoid. An adaptive fault tolerant controller is then developed to compensate for the failure effects on the system by estimating the fault and updating the design parameter matrices online. Both of these two controllers are in the form of a saturation avoidance feedback with the advantage of relatively small actuator capacities compared with the high gain counterpart. An example is included to illustrate the proposed procedures and their effectiveness.

Fault tolerant control for singular systems with actuator saturation and nonlinear perturbationFault tolerant control for singular systems with actuator saturation and nonlinear perturbation.

This paper is concerned with the stability analysis for continuous-time positive singular systems with time-varying delays. First, an auxiliary system is introduced to establish the positivity condition for singular time-delay systems. Based on the positivity condition, the stability criterion is obtained for the positive singular systems with constant delays. By analyzing the monotonic property of the system trajectory, we extend the stability condition to the cases with time-varying delays. A numerical simulation is employed to illustrate the effectiveness of our results.

Stability Analysis for Positive Singular Systems With Time-Varying Delays

State feedback controller design for singular positive Markovian jump systems with partly known transition rates

Positivity, exponential stability and disturbance attenuation performance for singular switched positive systems with time-varying distributed delays

On exponential stability of linear singular positive delayed systems

In this paper, we study the problem of passivity analysis of fractional-order neural networks (FONNs) with a time-varying delay. By using the Razumikhin fractional-order theorem, we first derive an improved sufficient criterion for asymptotic stability of FONNs with a bounded time-varying delay. Then, based on the proposed stability criterion and some auxiliary properties of fractional calculus, a delay-dependent condition is established to ensure the passivity of the considered system. These conditions are order-dependent and in the form of linear matrix inequalities, which therefore can be efficiently solved in polynomial time by using the existing convex algorithms. Some numerical examples are provided to show the effectiveness of the obtained results.

Passivity Analysis of Fractional-Order Neural Networks with Time-Varying Delay Based on LMI Approach

The problem of finite-time $$H_{\infty }$$ control for uncertain fractional-order neural networks is investigated in this paper. Using finite-time stability theory and the Lyapunov-like function method, we first derive a new condition for problem of finite-time stabilization of the considered fractional-order neural networks via linear matrix inequalities (LMIs). Then a new sufficient stabilization condition is proposed to ensure that the resulting closed-loop system is not only finite-time bounded but also satisfies finite-time $$H_{\infty }$$ performance. Three examples with simulations have been given to demonstrate the validity and correctness of the proposed methods.

Finite-time $$H_{\infty }$$H∞ control of uncertain fractional-order neural networks

This paper addresses the problem of unknown input fractional-order functional state observer design for a class of fractional-order time-delay nonlinear systems. The nonlinearities consist of two p...

Nguyen Huu Sau

Papers

On exponential stability of linear singular positive delayed systems

Passivity Analysis of Fractional-Order Neural Networks with Time-Varying Delay Based on LMI Approach

Finite-time $$H_{\infty }$$H∞ control of uncertain fractional-order neural networks

Unknown input fractional-order functional observer design for one-side Lipschitz time-delay fractional-order systems:

Positivity and stability analysis for linear implicit difference delay equations