Observer-Based Finite-Time Nonfragile Control for Nonlinear Systems With Actuator Saturation

2018 ◽  
Vol 14 (1) ◽  
Author(s):  
R. Sakthivel ◽  
R. Mohana Priya ◽  
Chao Wang ◽  
P. Dhanalakshmi
Keyword(s):  
Finite Time ◽  
Actuator Saturation ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Discrete Time System ◽  
Time Varying Delay ◽  
Control Gain ◽  
Finite Time Boundedness ◽  
Nonfragile Control

This paper considers a design problem of dissipative and observer-based finite-time nonfragile control for a class of uncertain discrete-time system with time-varying delay, nonlinearities, external disturbances, and actuator saturation. In particular, in this work, it is assumed that the nonlinearities satisfy Lipschitz condition for obtaining the required results. By choosing a suitable Lyapunov–Krasovskii functional, a new set of sufficient conditions is obtained in terms of linear matrix inequalities, which ensures the finite-time boundedness and dissipativeness of the resulting closed-loop system. Meanwhile, the solvability condition for the observer-based finite-time nonfragile control is also established, in which the control gain can be computed by solving a set of matrix inequalities. Finally, a numerical example based on the electric-hydraulic system is provided to illustrate the applicability of the developed control design technique.

Design the finite-time H∞ resilient filter of a class of switched systems with uncertain parameters

2017 ◽  
Vol 40 (9) ◽  
pp. 2756-2764 ◽  
Author(s):  
Qilong Ai ◽  
Chengcheng Ren ◽  
Jun Dong ◽  
Shuping He
Keyword(s):  
Dynamic Systems ◽  
Finite Time ◽  
Estimation Error ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Error Dynamic ◽  
Finite Time Boundedness ◽  
Error Dynamics

This paper is concerned with the problem of finite-time H∞ resilient filtering for a class of switch systems. The filtering error dynamics is constructed based on the H∞ resilient filter. The objective is to design a filter such that the finite-time H∞ gain from the unknown input to an estimation error is minimized or guaranteed to be less than or equal to a prescribed value. By selecting the proper multiple Lyapunov function and using the average dwell-time approach, sufficient conditions are obtained for the existence of the desired H∞ resilient filter, which also guarantee the finite-time boundedness of the filtering error dynamic systems. The design criteria are proposed in the form of linear matrix inequalities and then described as an optimization algorithm. Finally, a numerical example is employed to illustrate the effectiveness of the developed techniques.

Continuous-Time Feedback Control With Finite-Time Boundedness and H∞ Performance Criteria

2015 ◽  
Author(s):  
Jacob D. Hostettler ◽  
Xin Wang
Keyword(s):  
Feedback Control ◽  
Linear Matrix Inequalities ◽  
Finite Time ◽  
Control Method ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Performance Criteria ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Finite Time Boundedness

For advanced control applications, research into the use of linear matrix inequalities has yielded a notable amount of work in the area of nonlinear systems. Linear Matrix Inequalities can be formed through the application of desired performance criteria to a general system. By proper selection of a Lyapunov energy function, sufficient conditions to satisfy the performance objectives can be realized. The performance criteria, typically chosen for the application, define the objectives associated with the control. This work presents a control method for discrete-time systems with finite-time boundedness and H∞ performance criteria. The design of the controller corresponds to a system existing with bounded model uncertainties, and in the presence of L2 type external disturbances. Through the use of a linear state feedback control, sufficient conditions which guarantee the finite-time stability and H∞ performance objectives are achieved via the solution of a Linear Matrix Inequality. MATLAB application and simulation is carried out using the field oriented control of a permanent magnet synchronous generator in order to effectively demonstrate the effectiveness of this control strategy in the wind energy conversion system application.

scholarly journals Robust Finite-time Boundedness of Discrete-time Neural Networks with Time-varying Delays

2021 ◽  
Vol 17 ◽  
pp. 146-155
Author(s):  
Mengying Ding ◽  
Yali Dong
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Finite Time Stability ◽  
Time Varying Delay ◽  
Finite Time Boundedness ◽  
Varying Delay

This paper is concerned with the problem of robust finite-time boundedness for the discrete-time neural networks with time-varying delays. By constructing an appropriate Lyapunov-Krasovskii functional, we propose the sufficient conditions which ensure the robust finite-time boundedness of the discrete-time neural networks with time-varying delay in terms of linear matrix inequalities. Then the sufficient conditions of robust finite-time stability for the discrete-time neural networks with time-varying delays are given. Finally, a numerical example is presented to illustrate the efficiency of proposed methods.

scholarly journals Time-Varying Delayed H∞ Control Problem for Nonlinear Systems: A Finite Time Study Using Quadratic Convex Approach

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 713 ◽  
Author(s):  
Chanikan Emharuethai ◽  
Piyapong Niamsup ◽  
Raja Ramachandran ◽  
Wajaree Weera
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
State Feedback ◽  
Sufficient Conditions ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Time Varying ◽  
Time Varying Delay ◽  
Finite Time Boundedness ◽  
Varying Delay

In this manuscript, we consider the finite-time H ∞ control for nonlinear systems with time-varying delay. With the assistance of a novel Lyapunov-Krasovskii functional which includes some integral terms, a matrix-based on quadratic convex approach, combined with Wirtinger inequalities and some useful integral inequalities, a sufficient condition of finite-time boundedness is established. A novel feature presents in this paper is that the restriction which is necessary for the upper bound derivative is not restricted to less than 1. Further a H ∞ controller is designed via memoryless state feedback control and a new sufficient conditions for the existence of finite-time H ∞ state feedback for the system are given in terms of linear matrix inequalities (LMIs). At the end, some numerical examples with simulations are given to illustrate the effectiveness of the obtained result.

Exponential Stability for Stochastic Neural Networks with Time-Varying Delay and Leakage Delay

2015 ◽  
Vol 742 ◽  
pp. 399-403
Author(s):  
Ya Jun Li ◽  
Jing Zhao Li
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Leakage Delay ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Varying Delay

This paper investigates the exponential stability problem for a class of stochastic neural networks with leakage delay. By employing a suitable Lyapunov functional and stochastic stability theory technic, the sufficient conditions which make the stochastic neural networks system exponential mean square stable are proposed and proved. All results are expressed in terms of linear matrix inequalities (LMIs). Example and simulation are presented to show the effectiveness of the proposed method.

scholarly journals Finite-Time Stabilization for Stochastic Inertial Neural Networks with Time-Delay via Nonlinear Delay Controller

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Deyi Li ◽  
Yuanyuan Wang ◽  
Guici Chen ◽  
Shasha Zhu
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Finite Time ◽  
Design Method ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Nonlinear Feedback ◽  
Inertial Neural Networks ◽  
Finite Time Stabilization

This paper pays close attention to the problem of finite-time stabilization related to stochastic inertial neural networks with or without time-delay. By establishing proper Lyapunov-Krasovskii functional and making use of matrix inequalities, some sufficient conditions on finite-time stabilization are obtained and the stochastic settling-time function is also estimated. Furthermore, in order to achieve the finite-time stabilization, both delayed and nondelayed nonlinear feedback controllers are designed, respectively, in terms of solutions to a set of linear matrix inequalities (LMIs). Finally, a numerical example is provided to demonstrate the correction of the theoretical results and the effectiveness of the proposed control design method.

scholarly journals Dissipativity-Based Controller Design for Time-Delayed T-S Fuzzy Switched Distributed Parameter Systems

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Xiaona Song ◽  
Mi Wang ◽  
Shuai Song ◽  
Jingtao Man
Keyword(s):  
Fuzzy Controller ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Distributed Parameter Systems ◽  
Linear Matrix ◽  
Distributed Parameter ◽  
Time Varying Delay ◽  
Closed Loop Systems ◽  
Control Gain

This paper studies fuzzy controller design problem for a class of nonlinear switched distributed parameter systems (DPSs) subject to time-varying delay. Initially, the original nonlinear DPSs are accurately described by Takagi-Sugeno fuzzy model in a local region. On the basis of parallel distributed compensation technique, mode-dependent fuzzy proportional and fuzzy proportional-spatial-derivative controllers are constructed, respectively. Subsequently, using single Lyapunov-Krasovskii functional and some matrix inequality methods, sufficient conditions that guarantee the stability and dissipativity of the closed-loop systems are presented in the form of linear matrix inequalities, which allow the control gain matrices to be easily obtained. Finally, numerical examples are provided to demonstrate the validity of the designed controllers.

scholarly journals Guaranteed cost finite-time control of positive switched nonlinear systems with D-perturbation

2017 ◽  
Vol 15 (1) ◽  
pp. 1635-1648 ◽  
Author(s):  
Hao Xing ◽  
Leipo Liu ◽  
Xiangyang Cao ◽  
Zhumu Fu ◽  
Shuzhong Song
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Switched Nonlinear Systems ◽  
Time Varying Delay ◽  
Closed Loop Systems ◽  
Time Control ◽  
Guaranteed Cost ◽  
Finite Time Boundedness

Abstract This paper considers the guaranteed cost finite-time boundedness of positive switched nonlinear systems with D-perturbation and time-varying delay. Firstly, the definition of guaranteed cost finite-time boundedness is introduced. By using the Lyapunov-Krasovskii functional and average dwell time (ADT) approach, an output feedback controller is designed and sufficient conditions are obtained to ensure the corresponding closed-loop systems to be guaranteed cost finite-time boundedness (GCFTB). Such conditions can be solved by linear programming. Finally, two examples are provided to show the effectiveness of the proposed method.

Finite-time stability and finite-time boundedness of fractional order switched systems

2019 ◽  
Vol 41 (12) ◽  
pp. 3364-3371 ◽  
Author(s):  
Jinxia Liang ◽  
Baowei Wu ◽  
Lili Liu ◽  
Yue-E Wang ◽  
Changtao Li
Keyword(s):  
Fractional Order ◽  
Finite Time ◽  
Switched Systems ◽  
Sufficient Conditions ◽  
Average Dwell Time ◽  
Functional Method ◽  
Linear Matrix ◽  
Time Stability ◽  
Finite Time Stability ◽  
Finite Time Boundedness

Finite-time stability and finite-time boundedness of fractional order switched systems with [Formula: see text] are investigated in this paper. First of all, by employing the average dwell time technique and Lyapunov functional method, some sufficient conditions for finite-time stability and finite-time boundedness of fractional order switched systems are proposed. Furthermore, the state feedback controllers are constructed, and sufficient conditions are given to ensure that the corresponding closed-loop systems are finite-time stable and finite-time bounded. These conditions can be easily obtained in terms of linear matrix inequalities. Finally, two numerical examples are given to show the effectiveness of the results.

scholarly journals Finite-Time Synchronization of Complex Multilinks Networks with Perturbations and Time-Varying Delay Based on Nonlinear Adaptive Controller

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Lixiang Li ◽  
Qingbiao Liu ◽  
Tao Li
Keyword(s):  
Finite Time ◽  
Time Synchronization ◽  
Sufficient Conditions ◽  
Adaptive Controller ◽  
Linear Matrix ◽  
Time Varying ◽  
Finite Time Stability ◽  
Analytical Technique ◽  
Time Varying Delay ◽  
Product Inequality

This paper utilizes nonlinear adaptive feedback controller to make the complex multilinks networks with perturbations and time-varying delays achieve the finite-time synchronization. By designing nonlinear controllers, we use suitable Lyapunov functions and sufficient conditions to guarantee the finite-time synchronization between the drive system and the response system in terms of adaptive control. Several novel and useful finite-time synchronization criteria are accurately derived based on linear matrix inequality, Kronecker product, inequality analytical technique, and finite-time stability theory. Finally, numerical examples are given to demonstrate the validity and the effectiveness of our theoretical results.

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