scholarly journals RobustH∞Control for Spacecraft Rendezvous with a Noncooperative Target

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Shu-Nan Wu ◽  
Wen-Ya Zhou ◽  
Shu-Jun Tan ◽  
Guo-Qiang Wu
Keyword(s):  
Measurement Error ◽  
Relative Motion ◽  
Input Saturation ◽  
Uncertain System ◽  
Linear Matrix ◽  
Control Input ◽  
Sufficient Condition ◽  
Matrix Inequality ◽  
Time Performance ◽  
Saturation Measurement

The robustH∞control for spacecraft rendezvous with a noncooperative target is addressed in this paper. The relative motion of chaser and noncooperative target is firstly modeled as the uncertain system, which contains uncertain orbit parameter and mass. Then theH∞performance and finite time performance are proposed, and a robustH∞controller is developed to drive the chaser to rendezvous with the non-cooperative target in the presence of control input saturation, measurement error, and thrust error. The linear matrix inequality technology is used to derive the sufficient condition of the proposed controller. An illustrative example is finally provided to demonstrate the effectiveness of the controller.

On the Practical Stability of Incorporating Integral Compensation Into the Low-and-High Gain Control for a Class of Systems With Norm-Type Input Saturation

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Shou-Tao Peng
Keyword(s):  
Input Saturation ◽  
Gain Control ◽  
High Gain ◽  
Output Regulation ◽  
Practical Stability ◽  
Design Parameters ◽  
Linear Matrix ◽  
Control Input ◽  
Chattering Effect ◽  
Practical Stabilization

This paper studies the practical stability of incorporating integral compensation into the original low-and-high gain feedback law. The motivation for the incorporation is for achieving output regulation in the presence of constant disturbances without the use of a very large high-gain parameter required in the original approach. Due to numerical accuracy, the employment of very large high-gain parameters to eliminate steady-state error has the potential for inducing undesirable chattering effect on the control signal. A set of linear matrix inequalities is formulated in this study to obtain the related design parameters, by which the incorporation can achieve both the practical stabilization and asymptotic output regulation in the presence of input saturation and constant disturbances. Furthermore, the saturation of the control input can be shown to vanish in finite time during the process of regulation. Numerical examples are given to demonstrate the effectiveness of the proposed approach.

Unfragile Passive Control of Uncertain Sampling System

2013 ◽  
Vol 325-326 ◽  
pp. 1170-1175
Author(s):  
Qing Zhi Liu
Keyword(s):  
Control Problem ◽  
Robust Stability ◽  
Passive Control ◽  
Lyapunov Method ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequality ◽  
Sampling System ◽  
State Delay ◽  
Index Terms

The unfragile passive control problem of a class of uncertain state-delay sampling system is discussed. Applying Lyapunov method, and combining the properties of matrix inequality, the sufficient condition of robust stability is given, and the unfragile passive controller is designed. Finally a numerical example illustrates the effectiveness and the availability for the design.Index Terms - Uncertain State-delay Sampling System , Linear Matrix Inequility , Unfragile Passive Control .

Robust Control of Automotive Active Seat-Suspension System Subject to Actuator Saturation

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Zhou Gu ◽  
Shumin Fei ◽  
Yaqin Zhao ◽  
Engang Tian
Keyword(s):  
Controller Design ◽  
Actuator Saturation ◽  
Input Saturation ◽  
Output Feedback Control ◽  
Suspension System ◽  
Linear Matrix ◽  
Control Input ◽  
State Variables ◽  
Sampled Data ◽  
Seat Suspension

This paper deals with the problem of robust sampled-data control for an automotive seat-suspension system subject to control input saturation. By using the nature of the sector nonlinearity, a sampled-data based control input saturation in the control design is studied. A passenger dynamic behavior is considered in the modeling of seat-suspension system, which makes the model more precisely and brings about uncertainties as well in the developed model. Robust output feedback control strategy is adopted since some state variables, such as, body acceleration and body deflection, are unavailable. The desired controller can be achieved by solving the corresponding linear matrix inequalities (LMIs). Finally, a design example has been given to demonstrate the effectiveness and advantages of the proposed controller design approach.

Novel Approach to Robust Stability Criteria of Uncertain System with Time-Varying Delay

2013 ◽  
Vol 631-632 ◽  
pp. 1189-1194
Author(s):  
Chao Deng ◽  
Zhao Di Xu ◽  
Yu Bai ◽  
Xin Yuan Wang
Keyword(s):  
Linear Matrix Inequality ◽  
Robust Stability ◽  
Uncertain System ◽  
Linear Matrix ◽  
Convexity Property ◽  
Time Varying ◽  
Matrix Inequality ◽  
Stability Criteria ◽  
Time Varying Delay ◽  
Varying Delay

This paper considers the robust stability criteria of uncertain system with time-varying delay. Firstly, by exploiting a new Lyapunov function that optimizes the segment of time delay and using the convexity property and free-weight method of the Linear Matrix Inequality, delay-dependent stability condition can be obtained for the asymptotical stability of the nominal system. Secondly, basing on the obtained condition, the corresponding linear matrix inequality can be obtained for the uncertain system. Finally, an example is given to demostrate the effectiveness and the merit of the proposed method.

scholarly journals Delay-Dependent Stability of Uncertain Distributed Time-Delay Systems

2012 ◽  
Vol 6-7 ◽  
pp. 45-48
Author(s):  
Cheng Wang ◽  
Qing Zhang ◽  
Jian Ping Gan
Keyword(s):  
Time Delay ◽  
Delay Systems ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequality ◽  
Time Delay Systems ◽  
Parameter Uncertainties ◽  
Distributed Time Delay ◽  
Delay Dependent ◽  
Delay Dependent Stability

In this paper, the problem of stability analysis of uncertain distributed time-delay systems is investigated. Systems with norm-bounded parameter uncertainties are considered. By taking suitable Lyapunov-Krasovskii functional and free weighting matrices, a delay-dependent sufficient condition is derived in terms of linear matrix inequality (LMI). The condition obtained in this paper can be tested numerically very efficiently using interior point algorithms.

Observer Design for Lipschitz Nonlinear Systems with Output Uncertainty

2014 ◽  
Vol 533 ◽  
pp. 277-280
Author(s):  
Wei Zou ◽  
Yu Sheng Liu ◽  
Kai Liu
Keyword(s):  
Nonlinear Systems ◽  
Asymptotic Stability ◽  
Lyapunov Method ◽  
Observer Design ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequality ◽  
Output Uncertainty ◽  
Lipschitz Nonlinear Systems ◽  
Simulation Results

This paper presents an observer design for Lipschitz nonlinear systems with output uncertainty. By means of Lyapunov method as well as linear matrix inequality (LMI), the observer gain matrix is determined and a sufficient condition ensuring the asymptotic stability of the observer is proposed. Simulation results demonstrate the robustness of the proposed observer for output uncertainty.

Robust Stabilization of Uncertain Stochastic Systems with Delay in Control Input

2012 ◽  
Vol 461 ◽  
pp. 40-43 ◽  
Author(s):  
Cheng Wang
Keyword(s):  
Time Delay ◽  
Linear Matrix Inequality ◽  
Stochastic Systems ◽  
Robust Stabilization ◽  
Linear Matrix ◽  
Parametric Uncertainties ◽  
Control Input ◽  
Matrix Inequality ◽  
Stabilization Condition ◽  
Delay Dependent

This paper discusses the problems of robust stabilization of stochastic systems with parametric uncertainties and time delay in control input. The parametric uncertainties which appear in all system matrices are assumed to be norm bounded. The delay-dependent stabilization condition is derived by taking the relationships between terms in the Leibniz-Newton formula into account. Free-weighting matrices are employed to express these relationship, and the sufficient stabilization condition is formulated in terms of linear matrix inequality (LMI) based on the Lyapunov-Krasovskii theory, which can be solved by LMI toolbox in Matlab

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 Robust DistributedH∞Filtering for Nonlinear Systems with Sensor Saturations and Fractional Uncertainties with Digital Simulation

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Dong Liu ◽  
Guangfu Tang ◽  
Zhiyuan He ◽  
Yan Zhao ◽  
Hui Pang
Keyword(s):  
Nonlinear Systems ◽  
Linear Matrix Inequality ◽  
Digital Simulation ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequality ◽  
Parameter Uncertainties ◽  
Error System ◽  
Filtering Problem ◽  
Fractional Parameter

This paper is concerned with the robust distributedH∞filtering problem for nonlinear systems subject to sensor saturations and fractional parameter uncertainties. A sufficient condition is derived for the filtering error system to reach the requiredH∞performance in terms of recursive linear matrix inequality method. An iterative algorithm is then proposed to obtain the filter parameters recursively by solving the corresponding linear matrix inequality. A numerical example is presented to show the effectiveness of the proposed method.

On Proportional Plus Derivative State Feedback H2 Control for Descriptor Systems

2015 ◽  
pp. 146-172
Author(s):  
Rim Zaghdoud ◽  
Salah Salhi ◽  
Moufida Ksouri
Keyword(s):  
Singular Systems ◽  
Descriptor Systems ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequality ◽  
Stable States ◽  
H2 Control ◽  
Closed Loop Systems ◽  
Guaranteed Upper Bound ◽  
Necessary And Sufficient

This chapter studies the control problem for linear singular systems. Firstly a proportional plus derivative feedback controller for continuous and discrete cases for descriptor systems is given, satisfying the closed loop systems normal and stable states. A necessary and sufficient condition for the solvability of this problem should be obtained in terms of linear matrix inequality. In second part, the designed controller is required to yield a cost function with guaranteed upper bound for the continuous and discrete case and also an extension for robust control is developed. Numerical examples are included to show the effectiveness of the proposed result.

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