• International Journal of Control, Automation, and Systems
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• v.1 no.1
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• pp.11-18
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• 2003

The parametric approaches to sliding mode design are newly proposed for the class of multivariable systems. Our approach is based on an explicit formula for representing all the slid-ing modes using the Lyapunov matrices of full order. By manipulating Lyapunov matrices, the sliding modes which satisfy the design criteria such as the quadratic performance optimization and robust stability to parametric uncertainty, etc., can be easily obtained. The proposed ap-proach enables us to adopt a variety of Lyapunov- (or Riccati-) based approaches to the sliding mode design. Applications to the quadratic performance optimization problem, uncertain systems, systems with uncertain state delay, and the pole-clustering problem are discussed.

• International Journal of Control, Automation, and Systems
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• v.3 no.3
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• pp.397-402
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• 2005

The guaranteed cost control problem for a class of linear systems with norm-bounded time-varying parameter uncertainties and input constraints is considered. A sufficient condition for the existence of guaranteed cost state feedback controllers is derived via the linear matrix inequality (LMI) approach, and a design procedure to guaranteed cost controllers is given. Furthermore, a convex optimization problem is formulated to determine the optimal guaranteed cost controller. An example is given to illustrate the effectiveness of the proposed results.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.20 no.8
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• pp.710-716
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• 2010

This note represents a new disturbance observer to reduce effects of external disturbances. In case of conventional disturbance observers, additional stabilizing filters, so-called Q-filter, should be used because the conventional ones don't guarantee stability. But, the proposed one doesn't need the stabilizing filter, which is a fundamentally different research result from previous methods. Experimental verifications show this approach is realizable and valid to enhance precise positioning.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.53 no.1
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• pp.10-15
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• 2004

We present a state-space approach to make non-square linear systems strictly passive by using an input-dimensional parallel feedforward compensator. A necessary and sufficient condition for the existence of the parallel feedforward compensator is given by the static output feedback formulation, which enables to utilize linear matrix inequality. By modifying the structure of the compensator the additional technical assumption in the previous result [1] is removed. The effectiveness of the proposed method is illustrated by some numerical examples which can be stabilized by the proportional-derivative (PD) and proportional-derivative-integral (PID) control laws. The proposed control scheme can successfully replace the measurements of derivative terms in the control laws.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.63 no.7
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• pp.994-1000
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• 2014

This paper considers the problem of continuous and discrete time dissipative filter design method for the singular systems with polytopic uncertainties. Two bounded real lemmas (BRL) for the robust filters of dissipative singular systems along with the polytopic uncertainties are proposed on the basis of Lyapunov criterion. The sufficient conditions for both continuous and discrete time dissipative filter design methods are derived using the obtained BRL by linear matrix inequality (LMI) approach. Finally, the validities of the proposed methods are shown by numerical examples.

• Proceedings of the KIEE Conference
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• 2009.07a
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• pp.1724_1725
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• 2009

In this paper, new approaches to optimal controller design for a class of discrete-time Takagi-Sugeno (T-S) fuzzy systems are proposed based on a relaxed approach, in which non-quadratic Lyapunov function and non-parallel distributed compensation (PDC) control law are used. New relaxed conditions and linear matrix inequality (LMI) based design methods are proposed that allow outperforming previous results found in the literature. Finally, an example is given to demonstrate the efficiency of the proposed approaches.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.4
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• pp.617-621
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• 2012

This paper considers the synchronization problem of chaotic systems. For this problem, the sampled-data control approach is used to achieve asymptotic synchronization of two identical chaotic systems. Based on Lyapunov stability theory, a new stability condition is obtained via linear matrix inequality formulation to find the sampled-data feedback controller which achieves the synchronization between chaotic systems. Finally, the proposed method is applied to a numerical example in order to show the effectiveness of our results.

• International Journal of Control, Automation, and Systems
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• v.4 no.4
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• pp.516-523
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• 2006

This paper is concerned with the $H_{\infty}$ control problem of 2-D discrete state delay systems described by the Roesser model. The condition for the system to have a specified $H_{\infty}$ performance is derived via the linear matrix inequality (LMI) approach. Furthermore, a design procedure for $H_{\infty}$ state feedback controllers is given by solving a certain LMI. The design problem of optimal $H_{\infty}$ controllers is formulated as a convex optimization problem, which can be solved by existing convex optimization techniques. Simulation results are presented to illustrate the effectiveness of the proposed results.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.1492-1495
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• 2005

This paper presents a new linear-matrix-inequality-based intelligent digital redesign (LMI-based IDR) technique to match the states of the analog and the digital T-S fuzzy control systems at the intersampling instants as well as the sampling ones. The main features of the proposed technique are: 1) the affine control scheme is employed to increase the degree of freedom; 2) the fuzzy-model-based periodic control is employed; and the control input is changed n times during one sampling period; 3) The proposed IDR technique is based on the approximately discretized version of the T-S fuzzy system; but its discretization error vanishes as n approaches the infinity. 4) some sufficient conditions involved in the state matching and the stability of the closed-loop discrete-time system can be formulated in the LMIs format.

• Proceedings of the IEEK Conference
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• 1998.06a
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• pp.227-230
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• 1998

In this paper, we propose the design method of fuzzy robust H$\infty$ controller for the uncertain nonlinear discete-time systems with time delay. First, we represent a nonlinear plant with a modified T-S(Takagi-Sugeno) fuzzy model. Then design method utilizing the concept of PDC (parallel distributed compensation) is employed. For the modified T-S fuzzy model with uncertainty and delay, the sufficient condition of the quadratic stabilization with an H$\infty$ norm bound is presented in terms of Lyapunov stability theory and fuzzy robust H$\infty$ controller design method is given by LMI(linear matrix inequality) approach. Also an illustrative example is given to demonstrate the result of the proposed method.