Hinf Control of Uncertain Takagi-Sugeno Fuzzy Descriptor Systems

2013 ◽  
Vol 694-697 ◽  
pp. 2110-2115
Author(s):  
Bao Ping Ma ◽  
Ming Chen
Keyword(s):  
State Feedback ◽  
Descriptor Systems ◽  
Descriptor System ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Control Laws ◽  
Invariant Norm ◽  
Norm Bound ◽  
Takagi Sugeno ◽  
Time Invariant

This paper focuses on the problem of Hinf control for uncertain Takagi-Sugeno fuzzy descriptor system with time-invariant norm-bound uncertainty. Sufficient condition for robust Hinf control with state feedback is derived. It is shown that the control laws can be obtained by solving a set of linear matrix inequalities (LMIs) which is numerically tractable with commercially available software. Numerical example is given to demonstrate the advantage of the proposed method.

Admissible Conditions for T-S Fuzzy Descriptor Systems with Non-Differentiable Membership Functions

2013 ◽  
Vol 415 ◽  
pp. 259-266
Author(s):  
Peng Lin ◽  
Gang Hu
Keyword(s):  
Continuous Time ◽  
Lyapunov Functions ◽  
Closed Loop ◽  
Structural Information ◽  
Descriptor Systems ◽  
Linear Matrix ◽  
Membership Functions ◽  
Matrix Inequalities ◽  
Closed Loop Systems ◽  
Takagi Sugeno

In this paper, the admissible conditions (regular, impulse-free and stable) for a class of continuous-time Takagi-Sugeno (T-S) fuzzy descriptor systems are investigated. Sufficient admissible conditions for the closed-loop systems under non-parallel distributed compensation (non-PDC) feedback are proposed. This approach is mainly based on the state space division properly to make the membership functions continuous differentiable. Moreover, in order to make good use of the systems’ structural information in rules, the provided conditions are obtained through fuzzy Lyapunov functions candidate and can be formulated in terms of dilated Linear Matrix Inequalities (LMIs). Finally, the effectiveness of the proposed approach is shown through numerical example by using the optimization toolbox.

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.

scholarly journals Stability and stabilization of continuous descriptor systems: An LMI approach

2006 ◽  
Vol 2006 ◽  
pp. 1-15 ◽  
Author(s):  
M. Chaabane ◽  
O. Bachelier ◽  
M. Souissi ◽  
D. Mehdi
Keyword(s):  
State Feedback ◽  
Descriptor Systems ◽  
Descriptor System ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Necessary And Sufficient Condition ◽  
Lmi Approach ◽  
Stability And Stabilization ◽  
Necessary And Sufficient ◽  
Robust Stability And Stabilization

This paper deals with the problems of robust stability and stabilization for uncertain continuous descriptor systems. We propose a new necessary and sufficient condition in terms of a strict linear matrix inequality (LMI) for a nominal continuous descriptor system to be admissible (stable, regular, and impulse-free). Based on this, the state-feedback admissibility problem is solved and the solution is extended to the case of uncertain descriptor systems. Finally, numerical examples are given to illustrate the results.

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.

Fuzzy observer–based disturbance rejection control for nonlinear fractional-order systems with time-varying delay

2021 ◽  
pp. 107754632110069
Author(s):  
Parvin Mahmoudabadi ◽  
Mahsan Tavakoli-Kakhki
Keyword(s):  
Fractional Order ◽  
Disturbance Rejection ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Delayed Systems ◽  
Fuzzy Observer ◽  
Time Varying Delay ◽  
Takagi Sugeno

In this article, a Takagi–Sugeno fuzzy model is applied to deal with the problem of observer-based control design for nonlinear time-delayed systems with fractional-order [Formula: see text]. By applying the Lyapunov–Krasovskii method, a fuzzy observer–based controller is established to stabilize the time-delayed fractional-order Takagi–Sugeno fuzzy model. Also, the problem of disturbance rejection for the addressed systems is studied via the state-feedback method in the form of a parallel distributed compensation approach. Furthermore, sufficient conditions for the existence of state-feedback gains and observer gains are achieved in the terms of linear matrix inequalities. Finally, two numerical examples are simulated for the validation of the presented methods.

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.

scholarly journals Non-Fragile Robust H∞ Filtering of Takagi-Sugeno Fuzzy Networked Control Systems with Sensor Failures

Sensors ◽  
2019 ◽  
Vol 20 (1) ◽  
pp. 27 ◽  
Author(s):  
Hao Wang ◽  
Shousheng Xie ◽  
Bin Zhou ◽  
Weixuan Wang
Keyword(s):  
Control Systems ◽  
Networked Control Systems ◽  
Fault Tolerant ◽  
Fuzzy Model ◽  
Networked Control ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Sensor Failures ◽  
Takagi Sugeno ◽  
Filtering Problem

The fault-tolerant robust non-fragile H∞ filtering problem for networked control systems with sensor failures is studied in this paper. The Takagi-Sugeno fuzzy model which can appropriate any nonlinear systems is employed. Based on the model, a filter which can maintain stability and H∞ performance level under the influence of gain perturbation of the filter and sensor failures is designed. Moreover, the gain matrix of sensor failures is converted into a dynamic interval to expand the range of allowed failures. And the sufficient condition for the existence of the desired filter is derived in terms of linear matrix inequalities (LMIs) solutions. Finally a simulation example is given to illustrate the effectiveness of the proposed method.

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).

Sign in / Sign up

Export Citation Format

Share Document