This paper addresses the problem of dissipative-based stabilization for fractional-order nonlinear control systems with uncertainties, time-delay, external disturbances, actuator faults, actuator and sensor saturations. Specifically, a non-fragile reliable dynamic output feedback controller is designed for the purpose of stabilization of the addressed system. Due to the effect of saturation phenomena occurring in both the actuator and sensor, the anti-windup loops framed with the help of the observer design are incorporated into the controller design. Some sufficient conditions are formulated in terms of linear matrix inequalities by choosing a suitable Lyapunov function thereby assuring the dissipative-based stabilization. The derived results are thus validated by two numerical examples including the practical model of two-stage chemical reactor.

In this work, the stabilization of uncertain fractional-order dynamical control system with actuator faults and external disturbances will be addressed. Specifically, a fractional-order reset control system consisting of two sub-systems namely flow and jump subsystems will be designed. Based on the triggering conditions of reset law, a particular subsystem of the control system will be invoked. Meanwhile, the uncertainty and time-delay will be incorporated in the reset control system. Then the output of the reset control system, that is the control input of the system is designed to be fault-tolerant due to the presence of actuator faults. Further, the fractional-order dependent linear matrix inequalities (LMIs) will be derived by an appropriate choice of a Lyapunov function and other matrix inequalities. Thus, by solving the obtained LMIs, the gain values can be obtained guaranteeing the stabilization of the closed loop system with prescribed disturbance attenuation level. Later, the theoretical results are authenticated by providing numerical simulation results.

This paper discusses the stabilization issue for a class of nonlinear neutral-type stochastic systems subject to time-varying delays, linear fractional uncertainties, actuator faults, input saturation and fractional stochastic noise. Primarily, the derivation analysis for the stability and stabilization for the addressed systems is carried out by adopting a fractional infinitesimal operator. A fault-tolerant controller under saturation effect will be designed in order to guarantee the stabilization of the considered systems. Further, a set of stability criteria is obtained with the help of the fractional infinitesimal operator and by choosing a suitable Lyapunov-Krasovskii functional. These stability criteria are derived in the form of linear matrix inequalities that are solved by the MATLAB LMI toolbox. Finally, simulation results are provided to illustrate the effectiveness of our findings through a numerical example.

This study deals with the stabilisation problem of fractional-order time-delay systems with polytopic uncertainties and multiple disturbances with the use of Lyapunov stability theory. Notably, the multiple disturbances comprising both the known and unknown signals, are respectively characterised by the norm-bounded and exogenous system which signifies the harmonic signals with modelling perturbations. The control protocol is configured by the integration of proportional-retarded controller with gain perturbations and the output of an anti-disturbance observer. Precisely, the disturbance observer is taken into account for attenuating the influence of disturbance signals. Moreover, the implementation of a time-delay term in the feedback loop replicates the dynamic features of a derivative action that relies only on position measurements and its time differencing capabilities make it to be minimally sensitive against noise and provide a smoothing effect. By virtue of these circumstances, the asymptotic stability of the considered system is assured. With the aid of a suitable Lyapunov function, a set of robust order-dependent sufficient conditions is derived and then solved through the MATLAB LMI toolbox. As a result, the controller gain matrices can be computed and two numerical examples, including an electrical circuit model with simulation results are presented to certify the inherent potential of the theoretical outcomes.

This work discuss the stabilization issue for a class of fractional-order nonlinear systems together with time delay, parametric uncertainties and actuator faults. Precisely, the considered system comprises of two delays namely distributed delay and time-varying delay. Moreover, the occurrence of the actuator faults and fractional parametric uncertainties may induce poor performance of the systems. To overcome these issue, a non-fragile fault-tolerant controller is designed which makes the system asymptotically stable with the specified mixed $H_{\infty} $ and passive performance index. A fractional Razumikhin theorem is applied to handle the distributed delay term in the stabilization analysis. With the aid of suitable Lyapunov-Krasovskii functional, the sufficient conditions are established in terms of linear matrix inequalities together with Razumikhin stability theorem for getting the required results. By virtue of this, the controller gain matrix is obtained by solving the obtained LMIs and the graphical results are simulated using FOMCON toolbox. Later, the potency of the developed results are validated by virtue of three numerical examples including a rocket motor chamber.

This work focuses on the stabilization issue for a class of singular stochastic systems against fractional Gaussian noise driven by fractional Brownian motion. In particular, the system is formulated with time-delay, nonlinear actuator faults and randomly occurring parameter uncertainties. Primarily, a fractional-infinitesimal operator is incorporated to deal with the fractional Ito stochastic systems in the derivation part of Lyapunov-based stability analysis. Further, the considered system is subjected to both linear and nonlinear actuator faults and the stabilization will be achieved by the consideration of a nonlinear resilient fault-tolerant proportional-retarded controller. By incorporating the fractional-infinitesimal operator and with the choice of a relevant Lyapunov-Krasovskii functional candidate, a new adequate criterion is deduced by means of linear matrix inequalities. Then the established inequalities are then solved for obtaining the controller gain matrices. Thereafter, an example illustrating the effectiveness and applicability of the proposed results is provided.

This paper states with the objective of investigating the synchronization problem of nonlinear delayed fractional-order chaotic systems in conjunction with quantization, actuator faults, randomly occurring parametric uncertainties and exogenous disturbances. Moreover, the actuator faults are randomly occurring at any instant of time. The resultant random variables obeying Bernoulli distribution are introduced to account stochastic behavior. In spite of ensuring the robust performance, the finite-time synchronization of the addressed system is achieved and satisfies passive disturbance attenuation level by developing robust quantized stochastic reliable control protocol. As a consequence, the fast synchronization of the considered system is ensured in a finite time period. Owing to this perspective, the desired controller gain matrices can be obtained by solving developed linear matrix inequality. Further, the effectiveness of the theoretical result developed in this paper is validated via numerical simulation.

SummaryThis article focuses on a decentralized sampled‐data filter design for a class of large‐scale interconnected systems. Precisely in the addressed system, the inevitable factors such as missing measurements, time‐varying delays, randomly occurring uncertainties, and impulsive effects are taken into consideration. Also, we incorporated the gain perturbations and sensor faults in the proposed filter design. Furthermore, a new set of sufficient criterion has been derived by choosing an appropriate Lyapunov‐Krasovskii functional that ensures the asymptotic stability of the resulting augmented filtering error system with the prescribed mixed H∞ and passive performance index. Specifically, the corresponding filter gain matrices are derived by solving the developed sufficient criterion formulated in terms of linear matrix inequalities. The effectiveness of the proposed filter design technique are then exemplified by two numerical examples with simulations.