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, 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, the problem of finite-Time stability and finite-Time stabilization for a specific class of dynamical systems with nonlinear functions in the presence Time-varying delay and norm-bounded uncertainty terms is investigated. Nonlinear functions are considered to satisfy the Lipchitz conditions. At first, sufficient conditions to guarantee the finite-Time stability for Time-delay nonlinear system with uncertainties and based on the Lyapunov approach is presented. In the following, sufficient conditions to ensure finite Time stabilization the considered system with state feedback are presented. In the proofs of proposed theorems are used from the appropriate Lyapunov-Krasovskii function and newton-Libniz-formula that can reduce the conservative. Also, all of the obtained conditions in this paper are delay-dependent and presented as linear matrix inequalities. Finally, the numerical examples and simulations exhibit the effectiveness of the proposed methods.

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.

An adaptive input-output linearization method for general nonlinear systems is developed without using states of the system. Another key feature of this structure is the fact that, it does not need model of the system. In this scheme, neurolinearizer has few weights, so it is practical in adaptive situations. Online training of neurolinearizer is compared to model predictive recurrent training. Relationships between this controller and neural network based model reference adaptive controller are established. A CSTR reactor and pH control in a neutralization process illustrate performance of this method. Simulation studies show a superior performance with respect to a PI controller.

In this paper, Artificial Neural Networks are used to solve delay Differential Equations. We have suggested an appropriate approximation function based on ANN and then by solving an optimization problem of error function, the neural network is trained. The advantage of this technique is that the proposed approximation functions, with a slight modification, can be used for most types of delay differential equations, including DDE with constant delay, Time-dependent delay and pantograph delay. To demonstrate the effectiveness of the method, various examples have been tested and the validity and efficiency of the method have been shown.

This paper is concerned with the problem of delay-dependent passive analysis and control for interval stochastic Time-delay systems. The system matrices are assumed to be uncertain within given intervals, the Time delay is a Time-varying continuous function belonging to a given range, and the stochastic perturbation is in the form of a Brownian motion. By using ItO's differential formula and the Lyapunov stability theory, delay-dependent stochastic passive control criteria are proposed without ignoring any useful terms by considering the information of the lower bound and upper bound for the Time delay. Based on the criteria obtained, a delay-dependent passive controller that ensures the stochastic passivity of the closed-loop system is presented. Then, the controller gain is characterized in terms of LMIs, which can be easily checked by resorting to available software packages. Numerical examples are given to demonstrate the effectiveness of the method.

In this paper, a new approach for constructing quadratic Lyapunov-Krasovskii functionals for a class of nonlinear Time-delay systems is developed. The functionals are then used to derive delay dependent stability conditions. These conditions are sufficient and local. Numerical example shows that the results obtained using the proposed method is less conservative than those obtained by the existing methods.