Robust Decentralized Voltage Tracker of Islanded Multi-DG AC Microgrids Using Invariant Ellipsoids

This chapter develops a robust decentralized voltage tracker for islanded MGs. The proposed controller is robust against the plug and play operation of the MG, loads, and line parameter uncertainties. The problem is solved in the framework of linear matrix inequality (LMI). The proposed robust control represents the load changes and the parameter variations of lines connecting the DGs as a norm-bounded uncertainty. The proposed controller utilizes local measurements from DGs (i.e., it is totally decentralized). Control decentralization is accomplished by decomposing the global system into subsystems. The effect of the rest of the system on a specific subsystem is considered as a disturbance to minimize (disturbance rejection control). The controller is designed by the invariant-sets (approximated by the invariant ellipsoids). Different time-domain simulations are carried out as connecting and disconnected one or more DGs, connecting and disconnecting local loads DGs and transmission line parameters variation.

Synchronization of Fractional Order Uncertain BAM Competitive Neural Networks

This article examines the drive-response synchronization of a class of fractional order uncertain BAM (Bidirectional Associative Memory) competitive neural networks. By using the differential inclusions theory, and constructing a proper Lyapunov-Krasovskii functional, novel sufficient conditions are obtained to achieve global asymptotic stability of fractional order uncertain BAM competitive neural networks. This novel approach is based on the linear matrix inequality (LMI) technique and the derived conditions are easy to verify via the LMI toolbox. Moreover, numerical examples are presented to show the feasibility and effectiveness of the theoretical results.

Robust Exponential Stabilization for a Class of Nonlinear Uncertain Systems with Time-varying Delays

This paper is concerned with the problem of robust exponential stabilization for a class of nonlinear uncertain systems with time-varying delays. By using appropriately chosen Lyapunov-Krasovskii functional, together with the Finsler’s lemma, sufficient conditions for exponential stability of nonlinear uncertain systems with time-varying delays are proposed in terms of linear matrix inequality (LMI). Then, novel sufficient conditions are developed to ensure the nonlinear uncertain system with time-varying delay is robust exponentially stabilizable in terms of linear matrix inequality with state feedback control. Finally, a numerical example is given to illustrate the efficiency of proposed methods.

Fault detection in a three-tank hydraulic system using unknown input observer and extended Kalman filter

This paper presents the problem of fault diagnosis in a three-tank hydraulic system. A mathematical model of the system is developed in order to apply two different observing algorithms. Unknown Input Observer (UIO) and Extended Kalman Filter (EKF) have been used to detect and isolate actuator and sensor faults. For Unknown Input Observer (UIO), residuals are calculated from the measured and estimated output according to the eigenvalues of the system after processed by Linear Matrix Inequality (LMI). Extended Kalman filter uses process and measurement noise variances for state estimation. Unknown Input Observer and Extended Kalman Filter's performance in fault estimation and isolation is evaluated under different scenarios. Using Extended Kalman Filter (EKF), faults can be diagnosed effectively in the presence of noise, while Unknown Input Observer (UIO) is working better in the absence of noise, and simulation results illustrate that clearly.

Disturbance observer-based controller for inverted pendulum with uncertainties: Linear matrix inequality approach

<span lang="EN-US">A new approach based on linear matrix inequality (LMI) technique for stabilizing the inverted pendulum is developed in this article. The unknown states are estimated as well as the system is stabilized simultaneously by employing the observer-based controller. In addition, the impacts of the uncertainties are taken into consideration in this paper. Unlike the previous studies, the uncertainties in this study are unnecessary to satisfy the bounded constraints. These uncertainties will be converted into the unknown input disturbances, and then a disturbance observer-based controller will be synthesized to estimate the information of the unknown states, eliminate completely the effects of the uncertainties, and stabilize inverted pendulum system. With the support of lyapunov methodology, the conditions for constructing the observer and controller under the framework of linear matrix inequalities (LMIs) are derived in main theorems. Finally, the simulations for system with and without uncertainties are exhibited to show the merit and effectiveness of the proposed methods.</span>

Synthesis of Polynomial Fuzzy Model-Based Designs with Synchronization and Secure Communications for Chaos Systems with H∞ Performance

This paper presents the sum of squares (SOS)-based fuzzy control with H∞ performance for a synchronized chaos system and secure communications. To diminish the influence of the extrinsic perturbation, SOS-based stability criteria of the polynomial fuzzy system are derived by using the polynomial Lyapunov function. The perturbation decreasing achievement is indexed in a H∞ criterion. The submitted SOS-based stability criteria are more relaxed than the existing linear matrix inequality (LMI)-based stability criteria. The cryptography scheme based on an n-shift cipher is combined with synchronization for secure communications. Finally, numerical simulations illustrate the perturbation decay accomplishment of the submitted polynomial fuzzy compensator.

Robust Control of a Class of Nonlinear Discrete-Time Systems: Design and Experimental Results on a Real-Time Emulator

The aim of this study is to develop a new observer-based stabilization strategy for a class of Lipschitz uncertain systems. This new strategy improves the performances of existing methods and ensures better convergence conditions. Sliding window approach involves previous estimated states and measurements in the observer and the control law structures which increase the number of decision variables in the constraint to be solved and offers less restrictive Linear Matrix Inequality (LMI) conditions. The established sufficient stability conditions are in the form of Bilinear Matrix Inequality (BMI) which is solved in two steps. First, by using a slack variable technique and an appropriate reformulation of the Young’s inequality. Second, by introducing a useful approach to transform the obtained constraint to a more suitable one easily tractable by standard software algorithms. A comparison with the standard case is provided to show the superiority of the proposed H∞ observer-based controller which offers greater degree of freedom. The accuracy and the potential of the proposed process are shown through real time implementation of the one-link flexible joint robot to ARDUINO UNO R3 device and numerical comparison with some existing results.