• Proceedings of the KIEE Conference
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• 2000.07d
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• pp.2645-2647
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• 2000

This paper presents an LMI(Linear Matrix Inequalities) method for designing the optimal decoupling controller. The proposed controller based on the Two-Degree-of-Freedom configuration considers both the performance of controller and decoupling properties. The decoupling controller parameters are obtained from LMI method for computational efficiency.

• Transactions on Control, Automation and Systems Engineering
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• v.4 no.4
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• pp.356-362
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• 2002

In this paper, well-known Takagi-Sugeno fuzzy model is used as the nonlinear plant model and uncertainty is assumed to be included in the model structure with known bounds. Based on the fuzzy models, a numerical robust stability analysis for the fuzzy feedback linearization regulator is presented using Linear Matrix Inequalities (LMI) Theory. For these structured uncertainty, the closed system can be cast into Lur'e system by simple transformation. From the LMI stability condition for Lur'e system, we can derive the robust stability condition for the fuzzy feedback linearization regulator based on Takagi-Sugeno fuzzy model. The effectiveness of the proposed analysis is illustrated by a simple example.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.12 no.3
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• pp.187-192
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• 2012

This paper is concerned with stabilization problem of continuous-time Takagi-Sugeno fuzzy systems. To do this, the stabilization problem is investigated based on the new fuzzy Lyapunov functions (NFLFs). The NFLFs depend on not only the fuzzy weighting functions but also their first-time derivatives. The stabilization conditions are derived in terms of linear matrix inequalities (LMIs) which can be solved easily by the Matlab LMI Toolbox. Simulation examples are given to illustrate the effectiveness of this method.

• Journal of the Korean Institute of Intelligent Systems
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• v.16 no.4
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• pp.506-511
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• 2006

This paper considers a method to design sliding mode observers for a class of uncertain systems using Linear Matrix Inequalities(LMI). In an LMI-based sliding mode observer design method for a class of uncertain systems the switching surface is set to be the difference between the observer and system output. In terms of LMIs, a necessary and sufficient condition is derived for the existence of a sliding-mode observer guaranteeing a stable sliding motion on the switching surface. The gain matrices of the sliding-mode observer are characterized using the solution of the LMI existence condition. The results are illustrated by an example.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.39 no.3
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• pp.183-190
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• 2002

This paper describes the synthesis of robust and non-fragile H$\infty$ state feedback controllers for linear varying systems with affine parameter uncertainties, and static state feedback controller with structured uncertainty. The sufficient condition of controller existence, the design method of robust and non-fragile H$\infty$ static state feedback controller, and the set of controllers which satisfies non-fragility are presented. The obtained condition can be rewritten as parameterized Linear Matrix Inequalities(PLMls), that is, LMIs whose coefficients are functions of a parameter confined to a compact set. However, in contrast to LMIs, PLMIs feasibility problems involve infinitely many LMIs hence are inherently difficult to solve numerically. Therefore PLMls are transformed into standard LMI problems using relaxation techniques relying on separated convexity concepts. We show that the resulting controller guarantees the asymptotic stability and disturbance attenuation of the closed loop system in spite of controller gain variations within a degree.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.7
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• pp.1411-1417
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• 2009

In this paper, we consider the design of $H_{\infty}$ control of linear discrete-time systems having no mathematical model. The basic approach is to use Q-learning which is a reinforcement learning method based on actor-critic structure. The model-free control design is to use not the mathematical model of the system but the informations on states and inputs. As a result, the derived iterative algorithm is expressed as linear matrix inequalities(LMI) of measured data from system states and inputs. It is shown that, for a sufficiently rich enough disturbance, this algorithm converges to the standard $H_{\infty}$ control solution obtained using the exact system model. A simple numerical example is given to show the usefulness of our result on practical application.

• 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.

• Journal of the Korea Institute of Military Science and Technology
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• v.14 no.5
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• pp.941-947
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• 2011

This paper deals with the consensus problem for multi-agent linear dynamic systems with directed communication topology. All the agents are identical high-order linear systems and their state information is exchanged through a communication network with directed graph. It is shown that a consensus is achieved if there exists a feasible solution to a set of linear matrix inequalities obtained for a simultaneous stabilization problem for multiple systems. Examples are presented to show the effectiveness of the proposed method.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.11a
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• pp.91-94
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• 2005

This paper presents a new linear- matrix- inequality- basedintelligent digital redesign (LMI-based IDR) technique to match he states of the analog and the digital control systems at the intersampling instants as well as the sampling ones. The main features of the proposed technique are: 1) the multirate control is employed, and the control input is changed N times during one sampling period; 2) The proposed IDR technique is based on the compensated bilinear transformation.

• Journal of Institute of Control, Robotics and Systems
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• v.4 no.5
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• pp.592-599
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• 1998

In this paper, we design a tracking controller which satisfies transient response specifications and maintains tracking error within a tolerable limit for the uncertain track-following system of an optical disk drive. To this end, a robust $H_{\infty}$ control problem with regional stability constraints and sinusoidal disturbance rejection is considered. The internal model principle is used for rejecting the sinusoidal disturbance caused by eccentric rotation of the disk. We show that a condition satisfying the regional stability constraints can be expressed in terms of a linear matrix inequality (LMI) using the Lyapunov theory and S-procedure. Finally, a tracking controller is obtained by solving an LMI optimization problem involving two linear matrix inequalities. The proposed controller design method is evaluated through an experiment.