This research aims to investigate the stabilization of highly nonlinear hybrid stochastic differential Delay equations (HSDDEs) with L\'evy noise by Delay Feedback control. The coefficients of these systems satisfy a more general polynomial growth condition instead of classical linear growth condition. Precisely, an appropriate Lyapunov functional is constructed to analyze the stabilization of such systems in the sense of $H_{\infty}$-stability and asymptotic stability. The theoretical analysis indicates that the Delay can affect the stability of highly nonlinear hybrid stochastic systems.

In this paper, the chaotic dynamic analysis along with chaos controller of an active suspension in vehicle has been studied. The unstable periodic orbits of the system are stabilized using the developed Delay Feedback control algorithm based on the fuzzy sliding mode system. Firstly, the equations of model are derived via Newton-Euler rules and then, power spectrum density and bifurcation diagrams have been used to confirm chaos in the system. Variations of the control parameters in the bifurcation diagrams demonstrate the changes of system behavior from the periodic to the irregular chaotic responses. Finally, to eliminate the chaos in the vertical dynamics of vehicle, a novel fuzzy sliding Delay Feedback control algorithm is developed on the active suspension. Using fuzzy logic, the controller gain of the sliding Delay Feedback control is online estimated that is caused to reject the chattering phenomenon in the sliding mode algorithm beside the improvement of the responses. Simulation results of the control system depict a reduction of settling time and energy consumption along with eliminating the overshoots and chaotic vibrations.

This paper consists of two folds. At first, we deal with the stability analysis of a linear system of Delay differential equations. It is shown that the direct and cluster treatment methods are not applicable if there are some purely imaginary roots of the characteristic equation with multiplicity greater than one. To overcome the above difficulty, the system is decomposed into several subsystems. For the decomposition of a system, an invertible transformation is required to convert the matrices of the system into a block triangular (diagonal) form simultaneously. To achieve this goal, a necessary and sufficient condition is established. The second part concerns the stabilization of a linear system of Delay differential equations using the Delayed Feedback method and design a controller for generating the desired response. More precisely, the unstable poles of the linear system of Delay differential equations are moved to the left-half of the complex plane by the Delayed Feedback method. It is shown that the performance of the linear system of Delay differential equations can be improved by applying the Delayed Feedback method.

The chaotic dynamic analysis along with chaos controller of an active suspension in vehicles has been studied in this paper. The unstable periodic orbits of the system are stabilized using the developed Delay Feedback control algorithm based on the fuzzy sliding mode system. Firstly, the equations of motions in the chaotic half-vehicle model are derived via Newton-Euler rules and simulated by the fourth order Runge-Kutta method. Then, forcing frequency has been used to confirm nonlinear phenomenon such as jump and chaos in the vehicle system. Critical values of the control parameters in the forcing frequency demonstrate the changes of system behavior from the periodic to the irregular chaotic responses. In order to eliminate the chaotic behaviors in the vertical dynamics of vehicle, a novel fuzzy sliding Delay Feedback control algorithm is developed on the active suspension with chaotic responses. Using fuzzy logic, the controller gain of the sliding Delay Feedback control is online estimated that is caused to reject the chattering phenomenon in the sliding mode algorithm beside the improvement of the responses. Simulation results of the control system depict a reduction of settling time and energy consumption along with eliminating the overshoots and chaotic vibrations

In this paper, the optimal control algorithm design is proposed for droplet generation. In the proposed algorithm, the redundancy in the microfluidic channel network for droplet generation is used to the optimization setting in order to determine volume flow rate of fluid for each input channel; an optimization problem is proposed for minimizing the volume flow rate of fluid such that the droplet formed in the outlet channel is produced at the desired size. Also, due to the importance of estimating the system state, the design of the Luenberger observer (reduced order observer) has been developed. Then, the proposed scheme is robust against output Feedback Delay with respect to the optimal LQR control structure for tracking the desired value. While designing for the observer and controller sections, the Delays in the measurement of the output Feedback are considered, and the sustainability analysis for each of the sections has been performed due to the fixed Delay in the output Feedback. Output Feedback is a measurable variable of the input volume flow of each channel. Finally, the optimal control algorithm of droplet generation for a microfluidic structure with a T shape has been stimulated.

In this paper, we consider a general class of nonautonomous abstract Delayed evolution equations with a nonlinear source term. Under appropriate assumptions on the time-independent operator and the initial data, we establish global existence using the method of steps and employing classical results from the theory of inhomogeneous evolution problems. Then, by assuming that the operator associated with the non-Delayed part of the system generates an exponentially stable semigroup, we obtain an exponential decay estimate. This is achieved through a direct proof based on Duhamel's formula combined with Gronwall's inequality, under Lipschitz continuity conditions on the nonlinear source term. Finally, we conclude the paper by providing illustrative examples that validate the generalized setting of our system.

This study designs an observer for network- based distributed multi agent systems with interval time varying Delays in the presence of uncertainty and disturbances under a directed graph. A Delay interval partitioning method along with convex combination led to less conservative stability. In the presence of uncertainty and disturbances, using H¥ control along with dynamic output Feedback controller, robust observer and LMIs (Linear Matrix Inequalities) has led to better results in stability criteria and tracking the reference signal. Numerical examples are given to show the effectiveness of the obtained results.

This paper presents a novel Delay-dependent consensus algorithm within the linear matrix inequality (LMI) framework to solve consensus problem of linear multi-agent systems with time-varying communication and input Delays using fixed-order dynamic output Feedback controller. The proposed scheme is decentralized in the sense that each agent updates its state according to the output information of itself and its neighbors. To guarantee consensus in this method, first based on graph theory and by proper system transformations, the consensus problem is converted to the stability problem of an equivalent state-Delayed linear system. Then, by considering a suitable Lyapunov-Krasovskii function and applying special conditions on symmetric positive definite matrices, new Delay-dependent consensus criteria in LMI form and the unknown controller coefficients are obtained for the system under fixed interconnection topology which can be easily solved by various effective optimization algorithms. As a main feature of the proposed approach, the order of decentralized controllers can be chosen arbitrarily according to the system conditions and limitations. Finally, a numerical example is presented to show the applicability and effectiveness of the proposed method.

In this paper, we present a new method for solving fractional optimal control problems with Delays in state and control. This method is based upon Bernstein polynomials basis and Feedback control. The main advantage of Feedback or closed-loop control is that one can monitor the effect of such control on the system and modify the output accordingly. In this work, we use Bernstein polynomials to transform the fractional time-varying multi-dimensional optimal control system with both state and control Delays, into an algabric system in terms of the Bernstein coefficients approximating state and control functions. We use Caputo derivative of degree 0<a£1 as the fractional derivative in our work. Finally, some numerical examples are given to illustrate the effectiveness of this method.

In this paper, the design of a distributed adaptive controller for a class of unknown non-affine MIMO strict-Feedback multi agent systems with time Delay has been performed under a directed graph. The controller design is based on dynamic surface control method. In the design process, radial basis function neural networks (RBFNNs) were employed to approximate the unknown nonlinear functions. Stability analysis was performed using the Lyapunov-Krasovskii function and it was proved that all the signals of the closed-loop system are semi-globally uniformly bounded. Finally, the simulation results also confirmed the performance of the proposed control method.