• Journal of the Institute of Electronics Engineers of Korea SC
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• v.39 no.5
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• pp.18-25
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• 2002

In this paper, a novel computational approach for the stability analysis of the linguistic fuzzy system is proposed. The suggested analysis method is easily implemented by the recently spotlighted convex optimization techniques called Linear Matrix Inequalities (LMI). Compared with the previous works, the new method proposed herein is more relaxed and is applicable to not only the stabilization problem but also to the set-point regulation problem. Finally, the applicability of the suggested methodology is highlighted via computer simulations.

• Transactions on Control, Automation and Systems Engineering
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• v.4 no.4
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• pp.289-295
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• 2002

In this paper, a linear matrix inequality(LMI)-based robust control method, which combines model predictive control(MPC) with the feedback linearization(FL), is presented for constrained nonlinear systems with parameter uncertainty. The design procedures consist of the following 3 steps: Polytopic description of nonlinear system with a parameter uncertainty via FL, Mapping of actual input constraint by FL into constraint on new input of linearized system, Optimization of the constrained MPC problem based on LMI. To verify the performance and usefulness of the control method proposed in this paper, some simulations with application to a flexible single link manipulator are performed.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.3
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• pp.459-465
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• 2012

In this paper, we present a non-fragile guaranteed cost control design method for uncertain nonlinear systems with time varying delays in state and control input, even though the controller gain is perturbed. The uncertain nonlinear term in the systems is norm bounded and the linear matrix inequality(LMI) optimization method is employed as a stability analysis of the systems. We design a robust controller and show the asymptotical stability of uncertain time-varying systems based on Lyapunov method. Also, we guarantee a specific level of performance of the systems. The simulations are carried out to demonstrate the effectiveness of the proposed method.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.269-269
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• 2000

This paper presents a predictive control with H$_{\infty}$ suboptimal performance which is robust to disturbances and has a guaranteed stability. In order to derive the control law conveniently, state-space based approach, where the state variable is involved explicitly in the controller design and implementation is allowed. So an input-output model is converted to an equivalent observable canonical state-space form. The suggested control guarantees the norm bounded system output values from disturbances. A systematic way using the LMI method is presented to obtain appropriate parameters for Quadratic stability condition and optimization problem.

• 제어로봇시스템학회:학술대회논문집
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• 1998.10a
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• pp.151-156
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• 1998

In this paper, we present new control method for robot manipulators. The design objective can be the implementation of minimax controller with H$_{\infty}$ performance via LMI approach to guarantee the robustness and to obtain the exact tracking performance for robot manipulators with system parameter uncertainty and exogenous disturbance. We show that the Algebraic Riccati equation (ARE) which is needed for the construction of H$_{\infty}$ controller can be recast into the Algebraic Riccati Inequality (ARI) and the optimal control gain can be obtained by convex optimization method. Then, we will apply the proposed controller to rigid robot manipulators for verifying the performance of our controller.

• International Journal of Control, Automation, and Systems
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• v.6 no.1
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• pp.1-14
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• 2008

This paper presents a convex optimization method for observer-based mixed $H_2/H_{\infty}$ control design of linear systems with time-varying state, input and output delays. Delay-dependent sufficient conditions for the design of a desired observer-based control are given in terms of linear matrix inequalities (LMIs). An observer-based controller which guarantees asymptotic stability and a mixed $H_2/H_{\infty}$ performance for the closed-loop system of the linear system with time-varying delays is then developed. A Lyapunov-Krasovskii method underlies the observer-based mixed $H_2/H_{\infty}$ control design. A numerical example with simulation results illustrates the effectiveness of the methodology.

• Journal of Institute of Control, Robotics and Systems
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• v.13 no.6
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• pp.581-588
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• 2007

In this paper, we propose a delayed feedback guaranteed cost controller design method for linear time-delay systems with norm-bounded parameter uncertainties and nonlinear perturbations. A quadratic cost function is considered as the performance measure for the given system. Based on the Lyapunov method, an LMI optimization problem is formulated to design a controller such that the closed-loop cost function value is not more than a specified upper bound for all admissible system uncertainties and nonlinear perturbations. Numerical example show the effectiveness of the proposed method.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.8
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• pp.1491-1497
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• 2007

This paper considers robust and non-fragile guaranteed cost controller design method for descriptor systems with parameter uncertainties and time delay, and static state feedback controller with gain variations. The existence condition of controller, the design method of controller, the upper bound to minimize guaranteed cost function, and the measure of non-fragility in controller are proposed using linear matrix inequality (LMI) technique, which can be solved efficiently by convex optimization. Therefore, the presented robust and non-fragile guaranteed cost controller guarantees the asymptotic stability and non-fragility of the closed loop systems in spite of parameter uncertainties, time delay, and controller fragility.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2006.11a
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• pp.293-296
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• 2006

This paper presents new sufficient conditions to an intelligent digital redesign (IDR). The purpose of the IDR is to effectively convert an existing continuous-time fuzzy controller to an equivalent sampled-data fuzzy controller in the sense of the state-matching. The state-matching error between the closed-loop trajectories is carefully analyzed using the integral quadratic functional approach. The problem of designing the sampled-data fuzzy controller to minimize the state-matching error as well as to guarantee the stability is formulated and solved as the convex optimization problem with linear matrix inequality (LMI) constraints.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.8
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• pp.1353-1362
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• 2003

This paper considers a simultaneous optimization problem of structure and control systems. The problem is generally formulated as a non-convex optimization problem for the design parameters of mechanical structure and controller. Therefore, it is not easy to obtain the global solutions for practical problems. In this paper, we parameterize all design parameters of the mechanical structure such that the parameters work in the control system as decentralized static output feedback gains. Using this parameterization, we have formulated a simultaneous optimization problem in which the design specification is defined by the Η$_2$and Η$\_$$\infty$/ norms of the closed loop transfer function. So as to lead to a convex problem we approximate the nonlinear terms of design parameters to the linear terms. Then, we propose a convex optimization method that is based on linear matrix inequality (LMI). Using this method, we can surely obtain suboptimal solution for the design specification. A numerical example is given to illustrate the effectiveness of the proposed method.