Disturbance observer-based delayed robust feedback control design for a class of uncertain variable fractional-order systems: Order-dependent and delay-dependent stability.

This work addresses the stabilization of variable fractional-order (VFO) neutral-type systems with structure perturbations and unknown disturbance signals using the feedback control approach. The goal is to design disturbance-observer-based delayed state- and output-feedback controllers to achieve robust stability of such VFO systems. The proposed controller consists of two parts, namely a primary controller based on the linear feedback technique, and an auxiliary controller based on the disturbance observer. A disturbance observer is developed to estimate the disturbance signal, which is generated by an exogenous system. Based on matrix inequalities, order-dependent and delay-dependent conditions are formulated via FO Lyapunov theory that guarantee the robust stability of the closed-loop system. Simulations verify the main results.

Guaranteed cost-based feedback control design for fractional-order neutral systems with input-delayed and nonlinear perturbations.

Time delay in actuators is mainly caused by electrical and mechanical components. The effect is visible in the system response particularly when changing in the input command. Therefore, input delay is a problem in the control system design that must be taken into account. Besides, ignoring uncertainty in the dynamic models may compromise the controller design. Thus, how to mitigate the effect of this issue on the system stability and performance is a challenging topic. This article deals with the stabilization of fractional neutral systems considering input-delayed and nonlinear perturbations using the guaranteed cost-based feedback control technique. The main focus is to design the state- and output-feedback controllers to achieve a good performance. The stability criteria are formulated in the Lyapunov sense, which are described in terms of matrix inequalities. The proposed idea is validated using simulations.

LMI-Based Delayed Output Feedback Controller Design for a Class of Fractional-Order Neutral-Type Delay Systems Using Guaranteed Cost Control Approach.

In this research work, we deal with the stabilization of uncertain fractional-order neutral systems with delayed input. To tackle this problem, the guaranteed cost control method is considered. The purpose is to design a proportional-differential output feedback controller to obtain a satisfactory performance. The stability of the overall system is described in terms of matrix inequalities, and the corresponding analysis is performed in the perspective of Lyapunov's theory. Two application examples verify the analytic findings.

Robust stability of uncertain fractional order systems of neutral type with distributed delays and control input saturation.

Time delay occurs naturally due to the limited bandwidth of any real-world system. However, this problem can deteriorate the system performance and can even result in system instability. Input saturation is also an essential issue due to the energy constraint in real actuators that makes the control design procedure more difficult. This article concerns with the stability of uncertain fractional order (FO) delay systems of neutral type including structured uncertainties, distributed delays and actuator saturation. A Lyapunov-Krasovskii functional allows the formulation of the conditions to insure the asymptotic robust stability of such systems via the linear matrix inequalities (LMI) and to compute the gain of a state feedback controller. In addition, by using the cone complementarity linearization method, we obtain the controller gains that extend the domain of attraction. Several simulations validate the theoretical analysis.