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.

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.

scholarly journals Robust Finite-TimeH∞Control for Linear Time-Varying Descriptor Systems with Jumps

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Xiaoming Su ◽  
Adiya Bao
Keyword(s):  
Linear Matrix Inequalities ◽  
Finite Time ◽  
Linear Time ◽  
Descriptor Systems ◽  
Feasibility Problem ◽  
Descriptor System ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Finite Time Boundedness

The finite-timeH∞control problem is addressed for uncertain time-varying descriptor system with finite jumps and time-varying norm-bounded disturbance. Firstly, a sufficient condition of finite-time boundedness for the abovementioned class of system is obtained. Then the result is extended to finite-timeH∞for the system. Based on the condition, state feedback controller is designed such that the closed-loop system is finite-time boundedness and satisfiesL2gain. The conditions are given in terms of differential linear matrix inequalities (DLMIs) and linear matrix inequalities (LMIs), and such conditions require the solution of a feasibility problem involving DLMIs and LMIs, which can be solved by using existing linear algorithms. Finally, a numerical example is given to illustrate the effectiveness of the method.

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.

scholarly journals Finite-time non-fragile controller design for a class of switching linear parameter varying systems based on linear matrix inequalities

2018 ◽  
Vol 233 (1) ◽  
pp. 58-66 ◽  
Author(s):  
Chengcheng Ren ◽  
Longfang Li ◽  
Shuping He
Keyword(s):  
Linear Matrix Inequalities ◽  
Finite Time ◽  
Controller Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Parameter Varying ◽  
Linear Parameter Varying System

The finite-time non-fragile controller design problem is studied for a class of switching linear parameter varying system in this article. We aim to design a suitable finite-time non-fragile controller such that the closed-loop switching linear parameter varying system is finite-time bounded. Based on the linear matrix inequalities and multiple Lyapunov functions methods, sufficient conditions on the existence of the finite-time non-fragile controller are proposed and proved. Considering the parameters dependence, we change the infinite linear matrix inequalities into finite linear matrix inequalities by using approximate basis functions and gridding techniques. Finally, a simulation example is given to illustrate the effectiveness of the design 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.

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.

Sign in / Sign up

Export Citation Format

Share Document