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.

Stabilization Conditions for a Class of Fractional-Order Nonlinear Systems

2019 ◽  
Vol 14 (5) ◽  
Author(s):  
Sunhua Huang ◽  
Bin Wang
Keyword(s):  
Nonlinear Systems ◽  
Fractional Order ◽  
State Feedback ◽  
Closed Loop ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Lyapunov Stability Theorem ◽  
Matrix Inequalities ◽  
Feedback Controllers ◽  
Closed Loop Systems

The stabilization problem of fractional-order nonlinear systems for 0<α<1 is studied in this paper. Based on Mittag-Leffler function and the Lyapunov stability theorem, two practical stability conditions that ensure the stabilization of a class of fractional-order nonlinear systems are proposed. These stability conditions are given in terms of linear matrix inequalities and are easy to implement. Moreover, based on these conditions, the method for the design of state feedback controllers is given, and the conditions that enable the fractional-order nonlinear closed-loop systems to assure stability are provided. Finally, a representative case is employed to confirm the validity of the designed scheme.

Robust Reliable Sliding Mode H∞ Control for Uncertain Stochastic Nonlinear Jump Systems with Actuator Failures

2011 ◽  
Vol 480-481 ◽  
pp. 1475-1479
Author(s):  
Zhong Yi Tang ◽  
Sang Chen Ni ◽  
Wei Ping Duan
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Sliding Mode ◽  
Uncertain System ◽  
The State ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Sliding Surface ◽  
State Matrix ◽  
Actuator Failures

The problems of stochastic stability and robust reliable sliding mode H∞ control for a class of nonlinear matched and mismatched uncertain systems with stochastic jumps are considered in this paper. A more practical model of actuator failures than outage is considered. Based on the state feedback method, the resulting closed-loop systems are reliable in that they remain robust stochastically stable and satisfy a certain level of H∞ disturbance attenuation not only when all actuators are operational, but also in case of some actuator failures. The uncertain system under consideration may have mismatched norm bounded uncertainties in the state matrix. The transition of the jumping parameters in the systems is governed by a finite-state markov process. A sufficient condition is given for the existence of integral sliding surface in terms of linear matrix inequalities (LMIs). Then, a reaching motion controller is designed such that the resulting closed-loop system can be driven onto the desired sliding surface in finite time. Moreover, a state feedback controller is also constructed by using the solution of LMIS. Finally, we give a design example in order to show the effectiveness of our 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 StochasticH∞Control for Discrete-Time Singular Systems with State and Disturbance Dependent Noise

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Yong Zhao ◽  
Xiushan Jiang ◽  
Weihai Zhang
Keyword(s):  
Discrete Time ◽  
State Feedback ◽  
Closed Loop ◽  
Singular Systems ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Mean Square ◽  
Matrix Inequalities ◽  
Closed Loop System ◽  
Theoretical Results

This paper is concerned with the stochasticH∞state feedback control problem for a class of discrete-time singular systems with state and disturbance dependent noise. Two stochastic bounded real lemmas (SBRLs) are proposed via strict linear matrix inequalities (LMIs). Based on the obtained SBRLs, a state feedbackH∞controller is presented, which not only guarantees the resulting closed-loop system to be mean square admissible but also satisfies a prescribedH∞performance level. A numerical example is finally given to illustrate the effectiveness of the proposed theoretical results.

scholarly journals H∞Control for Network-Based 2D Systems with Missing Measurements

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Bu Xuhui ◽  
Wang Hongqi ◽  
Zheng Zheng ◽  
Qian Wei
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Control Law ◽  
2D Systems ◽  
Matrix Inequalities ◽  
Stochastic Variable ◽  
Missing Measurements ◽  
Binary Distribution

The problem ofH∞control for network-based 2D systems with missing measurements is considered. A stochastic variable satisfying the Bernoulli random binary distribution is utilized to characterize the missing measurements. Our attention is focused on the design of a state feedback controller such that the closed-loop 2D stochastic system is mean-square asymptotic stability and has an  H∞disturbance attenuation performance. A sufficient condition is established by means of linear matrix inequalities (LMIs) technique, and formulas can be given for the control law design. The result is also extended to more general cases where the system matrices contain uncertain parameters. Numerical examples are also given to illustrate the effectiveness of proposed approach.

scholarly journals Robust and NonfragileH∞Kalman-Type Filter Design for Parameter-Uncertain Time-Delay Systems: PLMI Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Seung Hyeop Yang ◽  
Hong Bae Park
Keyword(s):  
Time Delay ◽  
Linear Matrix Inequalities ◽  
Filter Design ◽  
Estimation Error ◽  
Delay Systems ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Time Delay Systems ◽  
Matrix Inequalities ◽  
Parameter Uncertainties

This paper describes the synthesis of a robust and nonfragileH∞Kalman-type filter design for a class of time-delay systems with polytopic uncertainties, filter-gain variations, and disturbances. We present the sufficient condition for filter existence and the method for designing a robust nonfragileH∞filter by using LMIs (Linear Matrix Inequalities) technique. Because the obtained sufficient condition can be represented as PLMIs (Parameterized Linear Matrix Inequalities), which can generate infinite LMIs, we use a relaxation technique to find finite solutions for a robust nonfragileH∞filter. We show that the proposed filter can minimize estimation error in terms of parameter uncertainties, filter-fragility, and disturbances.

Exponentially Dissipative Control for Singular Impulsive Dynamical Systems

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Li Yang ◽  
Xinzhi Liu ◽  
Zhigang Zhang
Keyword(s):  
Dynamical Systems ◽  
Linear Matrix Inequalities ◽  
State Feedback ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Closed Loop System ◽  
Dissipative Control ◽  
Necessary And Sufficient

This paper studies the problem of exponentially dissipative control for singular impulsive dynamical systems. Some necessary and sufficient conditions for exponential dissipativity of such systems are established in terms of linear matrix inequalities (LMIs). A state feedback controller is designed to make the closed-loop system exponentially dissipative. A numerical example is given to illustrate the feasibility of the method.

scholarly journals Robust Reliable Stabilization of Switched Nonlinear Systems with Time-Varying Delays and Delayed Switching

2010 ◽  
Vol 2010 ◽  
pp. 1-21 ◽  
Author(s):  
Zhengrong Xiang ◽  
Qingwei Chen
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
Linear Matrix ◽  
Time Varying ◽  
Switched Nonlinear Systems ◽  
Matrix Inequalities ◽  
Closed Loop System ◽  
Parameter Uncertainties ◽  
Actuator Failure ◽  
Exponentially Stable

This paper is concerned with the problem of robust reliable stabilization of switched nonlinear systems with time-varying delays and delayed switching is investigated. The parameter uncertainties are allowed to be norm-bounded. The switching instants of the controller experience delays with respect to those of the system. The purpose of this problem is to design a reliable state feedback controller such that, for all admissible parameter uncertainties and actuator failure, the system state of the closed-loop system is exponentially stable. We show that the addressed problem can be solved by means of algebraic matrix inequalities. The explicit expression of the desired robust controllers is derived in terms of linear matrix inequalities (LMIs).

Robust and Non-Fragile H∞ Observer-Based Filter Design for Parameter Uncertain System Using PLMI Approach

2013 ◽  
Vol 373-375 ◽  
pp. 685-688
Author(s):  
Seung Hyeop Yang ◽  
Seung Hyun Paik ◽  
Hong Bae Park
Keyword(s):  
Linear Matrix Inequalities ◽  
Filter Design ◽  
Estimation Error ◽  
Uncertain System ◽  
Relaxation Technique ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Polytopic Uncertainties

This paper describes the synthesis of a robust and non-fragile H∞ observer-based filter design for a class of parameter uncertain system with polytopic uncertainties, disturbances, and gain variations. We present the sufficient condition for filter existence and the method for designing a robust and non-fragile H∞ filter by using LMIs (Linear Matrix Inequalities) technique. Because the obtained sufficient condition can be represented as PLMIs (Parameterized Linear Matrix Inequalities), which can generate infinite LMIs, we use the relaxation technique to find finite solutions for a robust and non-fragile H∞ filter. We show that the proposed filter can minimize the estimation error in terms of parameter uncertainties, filter-fragility, and disturbances.

scholarly journals Finite-time stochastic input-to-state stability and observer-based controller design for singular nonlinear systems

2020 ◽  
Vol 25 (6) ◽  
pp. 980-996
Author(s):  
Feng Zhao ◽  
Xiangyong Chen ◽  
Jinde Cao ◽  
Ming Guo ◽  
Jianlong Qiu
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
State Feedback ◽  
Closed Loop ◽  
Controller Design ◽  
Linear Matrix ◽  
Stochastic Nonlinear Systems ◽  
Sufficient Condition ◽  
Exogenous Disturbance ◽  
Stochastic Input

This paper investigated observer-based controller for a class of singular nonlinear systems with state and exogenous disturbance-dependent noise. A new sufficient condition for finite-time stochastic input-to-state stability (FTSISS) of stochastic nonlinear systems is developed. Based on the sufficient condition, a sufficient condition on impulse-free and FTSISS for corresponding closed-loop error systems is provided. A linear matrix inequality condition, which can calculate the gains of the observer and state-feedback controller, is developed. Finally, two simulation examples are employed to demonstrate the effectiveness of the proposed approaches.

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