• Journal of Institute of Control, Robotics and Systems
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• v.13 no.9
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• pp.851-855
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• 2007

This paper deals with the problem of designing a linear sliding surface design for a class of uncertain systems with mismatched unstructured uncertainties. The uncertain system under consideration may have mismatched parameter uncertainties in the state matrix as well as in the input matrix. In terms of linear matrix inequalities (LMIs), we give a sufficient condition for the existence of linear sliding surfaces guaranteeing the asymptotic stability of the sliding mode dynamics. We show that our LMI condition can be less conservative than the existing conditions and our result supplement the existing results. Finally, we give a numerical example showing that our method can be better than the previous results.

• Journal of Institute of Control, Robotics and Systems
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• v.9 no.2
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• pp.117-123
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• 2003

Rotational machines such as optical disk drives, hard disk drives, and so on are subject to periodic disturbances caused by their mechanical characteristics. In the meanwhile, it is well known that repetitive control rejects periodic disturbance effectively. This paper presents a practical application of repetitive control to the track-following servo of an optical disk drive. The repetitive control system is composed of two repetitive controllers which compensate for periodic disturbances generated by track geometry and eccentric rotation of disk and a feedback controller stabilizing the feedback loop. A robust stability for all plant uncertainties is proved using linear matrix inequalities (LMIs). In the controller design, a weighting function is introduced for the feedback controller to ensure a minimum loop gain and a sufficient phase margin. The repetitive controllers and the feedback controller are designed by solving an optimization problem which can consider the robust stability condition and the system performance. The developed repetitive control system is implemented in the digital control system with a 16-bit fixed-point digital signal processor (DSP). Through simulation and experiment. The feasibility of the proposed repetitive control system is verified.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.5
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• pp.571-576
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• 2004

This paper presents a delay dependent fuzzy $H_{\infty}$ controller design method for delayed fuzzy dynamic systems. Using delay-dependent Lyapunov function, the global exponential stability and $H_{\infty}$ performance problem arc discussed. A sufficient conditions for the existence of fuzzy controller is presented in terms of linear matrix inequalities(LMIs). A simulation example is given to illustrate the design procedures and performances of the proposed methods.

• International Journal of Control, Automation, and Systems
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• v.3 no.2
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• pp.195-201
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• 2005

This paper discusses the problem of positive real control for uncertain 2-D linear discrete time singular Roesser models (2-D SRM) with time-invariant norm-bounded parameter uncertainty. The purpose of this study is to design a state feedback controller such that the resulting closed-loop system is acceptable, jump modes free and stable, and achieves the extended strictly positive realness for all admissible uncertainties. A version of positive real lemma for the 2-D SRM is given in terms of linear matrix inequalities (LMIs). Based on the lemma, a sufficient condition for the solvability of the positive real control problem is derived in terms of bilinear matrix inequalities (BMIs) and an iterative procedure for solving the BMIs is proposed.

• International Journal of Control, Automation, and Systems
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• v.4 no.6
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• pp.697-704
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• 2006

The paper is concerned with $H_{\infty}$ filtering for descriptor systems. A necessary and sufficient condition is established in terms of linear matrix inequalities(LMIs) for the existence of normal filters such that the error systems are admissible and the transfer function from the disturbance to the filtering error output satisfies a prescribed $H_{\infty}$-norm bound constraint. When these LMIs are feasible, an explicit parameterization expression of all desired normal filter is given. All these results are yielded without decomposing the original descriptor systems, which makes the filter design procedure simple and direct. Finally, a numerical example is derived to demonstrate the applicability of the proposed approach.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.81-84
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• 1997

This paper studies an active noise controller in a communication headset. The system is a two inputs(communication signal and noise signal) and single output(error signal) system. The problem is to reduce noise level sufficiently lower than communication signal to receive the communication signal clearly. The approach to this problem is in two steps. In the first step, we solve the noise rejection problem without communication signals. In this step, the problem is transformed to the robust H$_{\infty}$ regulating problem and solved using Linear Matrix Inequalities. In the second step, communication signal is introduced to the system, To verify the performance of the designed controller, a couple of experiments are performed..

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.2430-2434
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• 2003

This paper provides a new approach to analyze the stability of TCP Vegas, which is a kind of feedback-based congestion control algorithm. Whereas the conventional approaches use the approximately linearized model of the TCP Vegas along equilibrium points, this approach uses the exactly characterized dynamic model to get a new stability criterion via a piecewise and delay-dependent Lyapunov-Krasovskii function. Especially, the resulting stability criterion is formulated in terms of linear matrix inequalities (LMIs). Using the new criterion, this paper shows that the current TCP Vegas algorithm is stable in the sufficiently wide region of network delay and link capacity.

• Journal of Institute of Control, Robotics and Systems
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• v.10 no.7
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• pp.618-624
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• 2004

This paper presents a delay dependent fuzzy H_\infty$ filter design method for delayed fuzzy dynamic systems. Using delay-dependent Lyapunov function, the global exponential stability and H_\infty$ performance problem are discussed. A sufficient condition for the existence of fuzzy filter is presented in terms of linear matrix inequalities(LMIs). The filter design utilize the concept of parallel distributed compensation. And the filter gains can also be directly obtained from the LMI solutions. A simulation example is given to illustrate the design procedures and performance of the proposed methods.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.9
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• pp.1648-1654
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• 2007

In this paper, we consider the design of $H_\infty$ high-gain state feedback control for time-delayed linear systems with limited actuator capacities. The high-gain control means that the control permits the predetermined degree of saturation. Based on new Lyapunov-Krasovskii functional, we derive a result in the form of matrix inequalities. The matrix inequalities are consisted of LMIs those confirm the positive definiteness of Lyapunov- Krasovskii functional, satisfaction of predetermined degree of saturation, reachable set and $L_2$ gain constraint. The result is dependent on the bound of time-delay and its rate, predetermined degree of saturation, actuator capacity, and the allowed size of disturbances. Finally, we give a numerical example to show the effectiveness and usefulness of our result.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.326-330
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• 1998

There have been several recent studies concerning the stability of fuzzy control systems and the synthesis of stabilizing fuzzy controller. This paper reports on a related study of the TS(Takagi-Sugeno) fuzzy systems, and it is shown that the controller synthesis problems for the nonlinear systems described by the TS fuzzy model can be reduced to convex problems involving LMIs(Linear matrix inequalities). After classifying the TS fuzzy systems into two families based on how diverse their input matrices are, different controller synthesis procedure is given for each of these families. A numerical example is presented to illustrate the synthesis procedures developed in this paper.