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Robust H-infinity control for uncertain 2-D singular Roesser models

XU Hui-ling,SHENG Mei,ZOU Yun,GUO Lei,

控制理论与应用 , 2006,
Abstract: This paper discusses the problem of robust H-infinity control for linear discrete time 2-D singular Roesser models (2-D SRM) with parameter uncertainty. The purpose is the design of state feedback controllers such that the resulting closed-loop system is acceptable, jump modes free, stable and satisfies a specified H-infinity performance level for all admissible uncertainties. An equivalent form of bounded realness of 2-D SRM is established in terms of linear matrix inequalities. Based on this, a sufficient condition for the solvability of the robust H-infinity control problem for linear discrete time uncertain 2-D SRM is then presented, and a desired state feedback controller can also be derived by solving a set of matrix inequalities. Finally, numerical example is provided to demonstrate the applicability of the proposed approach.
A New Approach to Non-Fragile H Fuzzy Controller for Uncertain Fuzzy Dynamical Systems with Multiple Time-Scales
Wudhichai Assawinchaichote
International Journal of Systems Signal Control and Engineering Application , 2012, DOI: 10.3923/ijssceapp.2010.49.64
Abstract: This study examines the problem of designing a new approach to non-fragile H∞ controllers for a class of nonlinear uncertain dynamical systems with multiple time-scales described by a Takagi-Sugeno (TS) fuzzy model. Based on a Linear Matrix Inequality (LMI) approach, we develop a non-fragile H∞ controller which guarantees the L2-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value for this class of uncertain fuzzy dynamical systems with multiple time-scales. A numerical example is provided to illustrate the design developed in this study.
Robust Non-Fragile Control of 2-D Discrete Uncertain Systems: An LMI Approach  [PDF]
Paramanand Sharma, Amit Dhawan
Journal of Signal and Information Processing (JSIP) , 2012, DOI: 10.4236/jsip.2012.33049
Abstract: This paper considers the problem of robust non-fragile control for a class of two-dimensional (2-D) discrete uncertain systems described by the Fornasini-Marchesini second local state-space (FMSLSS) model under controller gain variations. The parameter uncertainty is assumed to be norm-bounded. The problem to be addressed is the design of non-fragile robust controllers via state feedback such that the resulting closed-loop system is asymptotically stable for all admissible parameter uncertainties and controller gain variations. A sufficient condition for the existence of such controllers is derived based on the linear matrix inequality (LMI) approach combined with the Lyapunov method. Finally, a numerical example is illustrated to show the contribution of the main result.
Robust reliable control of uncertain 2D discrete switched systems with state delays  [PDF]
Shipei Huang,Zhengrong Xiang
Mathematics , 2012,
Abstract: This paper is concerned with the problem of robust reliable control for a class of uncertain 2D discrete switched systems with state delays represented by a model of Roesser type. The parameter uncertainties are assumed to be norm-bounded. Firstly, delay-dependent sufficient condition for the exponential stability of the discrete 2D systems with state delays is established. Then, the concept of average dwell time is extended to 2D switched systems, and a reliable state feedback controller is developed in terms of linear matrix inequalities (LMIs) such that the resulting closed-loop system is exponentially stable for all admissible uncertainties and actuator failures. The dwell time approach is utilized for the stability analysis and controller design. Finally, an example is included to demonstrate the effectiveness of the proposed approach.
Optimal non-fragile guaranteed cost control for linear discrete-time systems with structured uncertainty

XIONG Jun-lin,ZHANG Qing-ling,

控制理论与应用 , 2004,
Abstract: The problem of the optimal non-fragile guaranteed cost control for uncertain linear discrete-time systems is considered. Both the system and the state feedback controller under consideration are assumed to have the time - varying structured uncertainties. Based on the linear matrix inequality technology, a sufficient condition is established to guarantee the existence of the desired non - fragile controllers and can be used to design such controllers. Two convex optimization algorithms are also proposed to select the optimal non - fragile controller in the sense of minimizing the upper bound of the quadratic performance index. A numerical example is given to show that the conservation of the upper bound is reduced by using the developed approach.
Non-fragile minimax control of nonlinear systems based on T-S model

JIANG Nan,JING Yuan-wei,
姜 囡

控制理论与应用 , 2008,
Abstract: To deal with the robust and non-fragile minimax control problem for uncertain nonlinear discrete systems, we construct a T-S model including the parametric uncertainty terms of the nonlinear systems to give a better approximation to the original system. The sufficient conditions for the existence of robust and non-fragile minimax control are derived in the sense of Lyapunov asymptotic stability and are formulated in the format of linear matrix inequalities (LMIs). The convex optimization algorithm is used to determine the minimal upper bound of the performance cost and the parameters of optimal minimax controller. The closed-loop system is asymptotically stable under the worst disturbances and the greatest uncertainty. An illustrative example of truck-trailer shows a good robust and non-fragile performance of the designed controller.
Non-Fragile Sliding Mode Control of Uncertain Chaotic Systems
Leipo Liu,Zhengzhi Han,Zhumu Fu
Journal of Control Science and Engineering , 2011, DOI: 10.1155/2011/859159
Abstract: This paper is concerned with non-fragile sliding mode control of uncertain chaotic systems with external disturbance. Firstly, a new sliding surface is proposed, and sufficient conditions are derived to guarantee that sliding mode dynamics is asymptotically stable with a generalized 2 disturbance rejection level. Secondly, non-fragile sliding mode controller is established to make the state of system reach the sliding surface in a finite time. Finally, an example is given to illustrate the effectiveness of the proposed method.
Design of robust non-fragile H-infinity controller based on Delta operator theory

Ruiquan LIN,Fuwen YANG,Qiugang CHEN,

控制理论与应用 , 2007,
Abstract: Considering that the controller parameters are of additive norm-bounded uncertainties when realized, a design method of robust non-fragile H-infinity controller for uncertain system based on Delta operator theory is illustrated in this paper. A sufficient and necessary condition of the existence for the controller is given, which is presented in LMI forms. Finally, the designed method is used in the speed control system of permanent magnet linear synchronous motor (PMLSM). With the designed controller, the resulted speed closed-loop system is still stable and has the expected Hinfinity performance even if the sample period is reduced and the parameters of the controller and the controlled object are of variations. The results show that the designed method is effective.
Robust non-fragile guaranteed-cost control for neutral systems with uncertain delay

FU Xing-jian,LIU Xiao-he,

控制理论与应用 , 2008,
Abstract: The robust non-fragile guaranteed-cost controller design for dynamic uncertain neutral systems with timedelay is considered. Both neutral systems and the state feedback controller are assumed to have the uncertainties. Based on the proper Lyapunov functions and linear matrix inequality, a sufficient condition is established to assure the neutral systems of quadratic stability and the existence of a robust non-fragile controller, with LMI depending on the size of the delay. By solving the corresponding linear matrix inequality, we obtain the robust non-fragile guaranteed-cost controller which can keep the quadratic performance function to stay in a given limit. Finally, a numerical simulation example is presented to illustrate the feasibility of this approach.
Delay-dependent Non-fragile H∞ Filtering for Uncertain Fuzzy Systems Based on a Switching Fuzzy Model and Piecewise Lyapunov Function
国际自动化与计算杂志 , 2010,
Abstract: This paper is concerned with the non-fragile H∞ filter design problem for uncertain discrete-time Takagi-Sugeno (T-S) fuzzy systems with time delay. To begin with, the T-S fuzzy system is transformed to an equivalent switching fuzzy system. Then, based on the piecewise Lyapunov function and matrix decoupling technique, a new delay-dependent non-fragile H∞ filtering method is proposed for the switching fuzzy system. The proposed condition is less conservative than the previous results. Since only a set of LMIs is involved, the filter parameters can be solved directly. Finally, a design example is provided to illustrate the validity of the proposed method.
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