Non-Fragile Robust H∞ Control for Linear Uncertain Switched Systems with Delayed Perturbations

2012 ◽  
Vol 562-564 ◽  
pp. 1968-1971
Author(s):  
Ze Yin Xu
Keyword(s):  
Switched Systems ◽  
State Feedback ◽  
Design Method ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Switching Strategy ◽  
Controller Gain ◽  
Simulation Results ◽  
Environment Parameters ◽  
The Given

The non-fragile robust H∞ controller was designed for a class of uncertain switched systems with delayed perturbations under additive perturbations of controller gain. A sufficient condition for the solvability of the non-fragile robust H∞ controller via state feedback was proved and presented, which based on a proper Lyapunov function and switching strategy, non-fragile robust H∞ controller can be obtained only by solving linear matrix inequalities. The systems under actions of the given controller are not only robust but also satisfy H∞ performance when controller changes, and thus have better adaptability against variety of the environment parameters. The simulation results show the effectiveness of the design method.

Multi-Model Adaptive Regulation for Aircraft Dynamics With Different Zero Structures

2014 ◽  
Author(s):  
Eric D. Peterson ◽  
Harry G. Kwatny
Keyword(s):  
State Feedback ◽  
Design Method ◽  
Linear Matrix ◽  
Model Design ◽  
Multiple Model ◽  
Matrix Inequalities ◽  
Adaptive Regulation ◽  
Aircraft Dynamics ◽  
Adaptive Regulator ◽  
Parameter Dependent

An adaptive regulator is designed for parameter dependent families of systems subject to changes in the zero structure. Since continuous adaptive regulation is limited by relative degree and right half plane zeros, a multiple model adaptive regulator is implemented. The two multiple model design subproblems, covering and switching, are addressed with LQR state feedback and Lyapunov function switch logic respectively. These two subproblems are combined into a set of Linear Matrix Inequalities (LMI) and concurrently solved. The multiple model design method is applied to longitudinal aircraft dynamics.

An LMI Approach to Guaranteed Cost Control of Networked Control Systems with Nonlinear Perturbation

2011 ◽  
Vol 480-481 ◽  
pp. 1352-1357
Author(s):  
Nan Xie ◽  
Bin Xia
Keyword(s):  
State Feedback ◽  
Controller Design ◽  
Networked Control Systems ◽  
Design Method ◽  
Networked Systems ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Quadratic Cost ◽  
Guaranteed Cost ◽  
Cone Complementarity Linearization

This paper is concerned with the problem of state-feedback guaranteed cost controller design for uncertain networked systems with both network-induces delay and data dropout taken into consideration. The sufficient condition for the existence of the networked guaranteed quadratic cost controller is obtained in terms of matrix inequalities, and the controller design method is deduced in terms of linear matrix inequalities. Furthermore, the suboptimal networked guaranteed cost controller design method is obtained with cone complementarity linearization algorithm. A numerical example is given to illustrate the proposed method.

scholarly journals On Designing Feedback Controllers for Master-Slave Synchronization of Memristor-Based Chua’s Circuits

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Ke Ding
Keyword(s):  
Linear Matrix Inequalities ◽  
Bounded Function ◽  
Design Method ◽  
Quadratic Functions ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Feedback Controllers ◽  
Piecewise Constant ◽  
Controller Gain ◽  
Bounded Derivative

This paper is concerned with designing feedback controllers for master-slave synchronization of two chaotic memristor-based Chua’s circuits. The memductance function of memristor-based Chua’s circuits is a bounded function with a bounded derivative which is more generalized than those piecewise constant-valued functions or quadratic functions in some existing papers. The main contributions are that one master-slave synchronization criterion is established for two chaotic memristor-based Chua’s circuits, and the feedback controller gain is easily obtained by solving a set of linear matrix inequalities. One numerical example is given to illustrate the effectiveness of the design method.

scholarly journals Simultaneous Fault Detection and Control for Discrete-Time Systems via a Switched Scheme

2015 ◽  
Vol 2015 ◽  
pp. 1-13
Author(s):  
Jian Li ◽  
Xingze Dai
Keyword(s):  
Fault Detection ◽  
Design Method ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Switching Strategy ◽  
Discrete Time Systems ◽  
Step Procedure ◽  
Control Objective ◽  
And Control ◽  
Time Systems

This paper is concerned with the problem of simultaneous fault detection and control for linear systems with a switched scheme. The switched detector/controller is designed simultaneously and generates two signals such that it provides fault tolerance, especially including “destabilizing failure” meanwhile, it generates the residual signal to alarm the fault. When the faults are detected, the detector/controller is switched to reduce the effect of the faults. When the faults are removed, the detector/controller is switched to the original detector/controller to guarantee the control objective. In addition, it has time delay in detection of the faults; then the time-driven switching strategy for asynchronous case is included. Thus a mixed switching strategy is proposed. A two-step procedure is adopted to obtain the solutions through satisfying a set of linear matrix inequalities. Finally, an example is provided to demonstrate the effectiveness of the proposed design method.

scholarly journals Optimal Fuzzy Control for a Class of Nonlinear Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-29 ◽  
Author(s):  
Dušan Krokavec ◽  
Anna Filasová
Keyword(s):  
Nonlinear Systems ◽  
Design Method ◽  
Design Procedure ◽  
Control Design ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Stabilizing Controllers ◽  
Simulation Results ◽  
Takagi Sugeno ◽  
Slack Matrices

The paper presents conditions suitable in design giving quadratic performances to stabilizing controllers for given class of continuous-time nonlinear systems, represented by Takagi-Sugeno models. Based on extended Lyapunov function and slack matrices, the design conditions are outlined in the terms of linear matrix inequalities to possess a stable structure closest to LQ performance, if premise variables are measurable. Simulation results illustrate the design procedure and demonstrate the performances of the proposed control design method.

State Feedback Robust H∞ Control for Generalized Discrete System and Simulation

2013 ◽  
Vol 467 ◽  
pp. 621-626
Author(s):  
Chen Fang ◽  
Jiang Hong Shi ◽  
Kun Yu Li ◽  
Zheng Wang
Keyword(s):  
Discrete System ◽  
State Feedback ◽  
Closed Loop ◽  
The State ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Robust Controller ◽  
Closed Loop Systems

For a class of uncertain generalized discrete linear system with norm-bounded parameter uncertainties, the state feedback robust control problem is studied. One sufficient condition for the solvability of the problem and the state feedback robust controller are obtained in terms of linear matrix inequalities. The designed controller guarantees that the closed-loop systems is regular, causal, stable and satisfies a prescribed norm bounded constraint for all admissible uncertain parameters under some conditions. The result of the normal discrete system can be regarded as a particular form of our conclusion. A simulation example is given to demonstrate 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 Fuzzy Controllers for Nonaffine-in-Control Singularly Perturbed Switched Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Linna Zhou ◽  
Qianjin Wang ◽  
Xiaoping Ma ◽  
Chunyu Yang
Keyword(s):  
Switched Systems ◽  
Fuzzy Controller ◽  
Controller Design ◽  
Design Method ◽  
Singularly Perturbed ◽  
Dynamic State ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Stability Bound ◽  
Takagi Sugeno

This paper investigates the problem of fuzzy controller design for nonaffine-in-control singularly perturbed switched systems (NCSPSSs). First, the NCSPSS is approximated by Takagi-Sugeno (T-S) models which include not only state but also control variables in the premise part of the rules. Then, a dynamic state feedback controller design method is proposed in terms of linear matrix inequalities. Under the controller, stability bound estimation problem of the closed-loop system is solved. Finally, an example is given to show the feasibility and effectiveness of the obtained methods.

Further Results on Exponential Stability and State Feedback Stabilization for Time Delay Singular Saturating Actuator Systems With Delay-Dependence

2017 ◽  
Vol 139 (10) ◽  
Author(s):  
Pin-Lin Liu
Keyword(s):  
Time Delay ◽  
Convex Optimization ◽  
State Feedback ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Feedback Stabilization ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Decision Variables ◽  
Delay Dependence

This paper will study the exponential stable and state feedback stabilization of time delay singular systems with saturation actuators. Some sufficient conditions for existence of controller are obtained by using the linear matrix inequalities (LMIs) and integral inequality approach (IIA). When these LMIs are feasible, an explicit expression of controller is obtained. Based on Lyapunov–Krasovskii functional (LKF) techniques, a novel exponential stabilization criterion has been also derived in terms of LMIs which can be easily solved with efficient convex optimization algorithm. Our results are less conservative than some existing ones, and the decision variables involved in this paper are less than them. Examples illustrate our results as less conservative than those reported in the literature.

Mixed H2/H∞ Control for State-Delayed Linear Systems and a LMI Approach to the Solution of Coupled AREs

2003 ◽  
Vol 125 (2) ◽  
pp. 249-253 ◽  
Author(s):  
M. D. S. Aliyu
Keyword(s):  
Control Problem ◽  
Linear Systems ◽  
Linear Matrix Inequalities ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Riccati Equations ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Lmi Approach ◽  
Alternative Approach

In this paper, the state-feedback mixed H2/H∞ control problem for state-delayed linear systems is considered. Sufficient conditions for the solvability of this problem are given in terms of the solution to a pair of algebraic Riccati equations similar to the nondelayed case. However, these Riccati equations are more difficult to solve than those arising in the pure H2,H∞ problems, and an alternative approach is to solve a pair of linear matrix inequalities (LMIs).

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