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1
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LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties

100%
Balasubramaniam P., Lakshmanan S., Rakkiyappan R.
International Journal of Applied Mathematics and Computer Science
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2012
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tom 22
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nr 2
339-351
EN
This paper studies an LMI optimization problem of delay-dependent robust stability criteria for stochastic systems with polytopic and linear fractional uncertainties. The delay is assumed to be time-varying and belong to a given interval, which means that lower and upper bounds of this interval time-varying delay are available. The uncertainty under consideration includes polytopic-type uncertainty and linear fractional norm-bounded uncertainty. Based on the new Lyapunov-Krasovskii functional, some inequality techniques and stochastic stability theory, delay-dependent stability criteria are obtained in terms of Linear Matrix Inequalities (LMIs). Moreover, the derivative of time delays is allowed to take any value. Finally, four numerical examples are given to illustrate the effectiveness of the proposed method and to show an improvement over some results found in the literature.
2
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Fault-tolerant control strategy for actuator faults using LPV techniques: Application to a two degree of freedom helicopter

100%
Montes de Oca S., Puig V., Witczak M., Dziekan Ł.
International Journal of Applied Mathematics and Computer Science
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2012
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tom 22
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nr 1
161-171
EN
In this paper, a Fault Tolerant Control (FTC) strategy for Linear Parameter Varying (LPV) systems that can be used in the case of actuator faults is proposed. The idea of this FTC method is to adapt the faulty plant instead of adapting the controller to the faulty plant. This approach can be seen as a kind of virtual actuator. An integrated FTC design procedure for the fault identification and fault-tolerant control schemes using LPV techniques is provided as well. Fault identification is based on the use of an Unknown Input Observer (UIO). The FTC controller is implemented as a state feedback controller and designed using polytopic LPV techniques and Linear Matrix Inequality (LMI) regions in such a way as to guarantee the closed-loop behavior in terms of several LMI constraints. To assess the performance of the proposed approach, a two degree of freedom helicopter is used.
3
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A 2D system approach to the design of a robust modified repetitive-control system with a dynamic output-feedback controller

88%
Zhou L., She J., Zhou S.
International Journal of Applied Mathematics and Computer Science
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2014
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tom 24
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nr 2
325-334
EN
This paper is concerned with the problem of designing a robust modified repetitive-control system with a dynamic outputfeedback controller for a class of strictly proper plants. Employing the continuous lifting technique, a continuous-discrete two-dimensional (2D) model is built that accurately describes the features of repetitive control. The 2D control input contains the direct sum of the effects of control and learning, which allows us to adjust control and learning preferentially. The singular-value decomposition of the output matrix and Lyapunov stability theory are used to derive an asymptotic stability condition based on a Linear Matrix Inequality (LMI). Two tuning parameters in the LMI manipulate the preferential adjustment of control and learning. A numerical example illustrates the tuning procedure and demonstrates the effectiveness of the method.
4
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Robust aperiodic-disturbance rejection in an uncertain modified repetitive-control system

88%
Zhou L., She J., Li C., Pan C.
International Journal of Applied Mathematics and Computer Science
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2016
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tom 26
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nr 2
285-295
EN
This paper concerns the problem of designing an EID-based robust output-feedback modified repetitive-control system (ROFMRCS) that provides satisfactory aperiodic-disturbance rejection performance for a class of plants with time-varying structured uncertainties. An equivalent-input-disturbance (EID) estimator is added to the ROFMRCS that estimates the influences of all types of disturbances and compensates them. A continuous-discrete two-dimensional model is built to describe the EID-based ROFMRCS that accurately presents the features of repetitive control, thereby enabling the control and learning actions to be preferentially adjusted. A robust stability condition for the closed-loop system is given in terms of a linear matrix inequality. It yields the parameters of the repetitive controller, the output-feedback controller, and the EID-estimator. Finally, a numerical example demonstrates the validity of the method.
5
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An LPV pole-placement approach to friction compensation as an FTC problem

88%
Patton R., Chen L., Klinkhieo S.
International Journal of Applied Mathematics and Computer Science
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2012
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tom 22
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nr 1
149-160
EN
The concept of combining robust fault estimation within a controller system to achieve active Fault Tolerant Control (FTC) has been the subject of considerable interest in the recent literature. The current study is motivated by the need to develop model-based FTC schemes for systems that have no unique equilibria and are therefore difficult to linearise. Linear Parameter Varying (LPV) strategies are well suited to model-based control and fault estimation for such systems. This contribution involves pole-placement within suitable LMI regions, guaranteeing both stability and performance of a multi-fault LPV estimator employed within an FTC structure. The proposed design strategy is illustrated using a nonlinear two-link manipulator system with friction forces acting simultaneously at each joint. The friction forces, regarded as a special case of actuator faults, are estimated and their effect is compensated within a polytope controller system, yielding a robust form of active FTC that is easy to apply to real robot systems.
6
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Delay-dependent generalized H₂ control for discrete T-S fuzzy large-scale stochastic systems with mixed delays

88%
Li J., Li J., Xia Z.
International Journal of Applied Mathematics and Computer Science
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2011
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tom 21
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nr 4
585-603
EN
This paper is concerned with the problem of stochastic stability and generalized H₂ control for discrete-time fuzzy largescale stochastic systems with time-varying and infinite-distributed delays. Large-scale interconnected systems consist of a number of discrete-time interconnected Takagi-Sugeno (T-S) subsystems. First, a novel Delay-Dependent Piecewise Lyapunov-Krasovskii Functional (DDPLKF) is proposed, in which both the upper and the lower bound of delays are considered. Then, two improved delay-dependent stability conditions are established based on this DDPLKF in terms of Linear Matrix Inequalities (LMIs). The merit of the proposed conditions lies in its reduced conservatism, which is achieved by circumventing the utilization of some bounding inequalities for cross products of two vectors and by considering the interactions among the fuzzy subsystems in each subregion. A decentralized generalized H₂ state feedback fuzzy controller is designed for each subsystem. It is shown that the mean-square stability for discrete T-S fuzzy large-scale stochastic systems can be established if a DDPLKF can be constructed and a decentralized controller can be obtained by solving a set of LMIs. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed method.
7
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$H_∞$ control of discrete-time linear systems constrained in state by equality constraints

75%
Krokavec D.
International Journal of Applied Mathematics and Computer Science
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2012
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tom 22
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nr 3
551-560
EN
In this paper, stabilizing problems in control design are addressed for linear discrete-time systems, reflecting equality constraints tying together some state variables. Based on an enhanced representation of the bounded real lemma for discretetime systems, the existence of a state feedback control for such conditioned stabilization is proven, and an LMI-based design procedure is provided. The control law gain computation method used circumvents generally an ill-conditioned singular design task. The principle, when compared with previously published results, indicates that the proposed method outperforms the existing approaches, guarantees feasibility, and improves the steady-state accuracy of the control. Furthermore, better performance is achieved with essentially reduced design effort. The approach is illustrated on simulation examples, where the validity of the proposed method is demonstrated using one state equality constraint.
8
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Design of unknown input fractional-order observers for fractional-order systems

75%
N'Doye I., Darouach M., Voos H., Zasadzinski M.
International Journal of Applied Mathematics and Computer Science
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2013
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tom 23
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nr 3
491-500
EN
This paper considers a method of designing fractional-order observers for continuous-time linear fractional-order systems with unknown inputs. Conditions for the existence of these observers are given. Sufficient conditions for the asymptotical stability of fractional-order observer errors with the fractional order α satisfying 0 < α < 2 are derived in terms of linear matrix inequalities. Two numerical examples are given to demonstrate the applicability of the proposed approach, where the fractional order α belongs to 1 ≤ α < 2 and 0 < α ≤ 1, respectively. A stability analysis of the fractional-order error system is made and it is shown that the fractional-order observers are as stable as their integer order counterpart and guarantee better convergence of the estimation error.
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