• The Transactions of the Korean Institute of Electrical Engineers A
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• v.48 no.5
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• pp.560-570
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• 1999

This paper formulates the suboptimal robust Kalman filtering problem into two coupled Linear Matrix Inequality (LMI) problems by applying Lyapunov theory to the augmented system which is composed of the state equation in the uncertain linear system and the estimation error dynamics. This formulations not only provide the sufficient conditions for the existence of the desired filter, but also construct the suboptimal robust Kalman filter. The proposed filter can guarantee the optimized upper bound of the estimation error variance for uncertain systems with parametric uncertainties in both the state and measurement matrices. In addition, this paper shows how the problem of finding the minimizing solution subject to Quadratic Matrix Inequality (QMI), which cannot be easily transformed into LMI using the usual Schur complement formula, can be successfully modified into a generic LMI problem.

• Journal of Advanced Marine Engineering and Technology
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• v.25 no.2
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• pp.321-330
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• 2001

Magnetic bearing system is frequently used for high-speed rotating machines because of its frictionless property. But the magnetic bearing system needs feedback controller for stabilization. This paper presents a robust controller design by using linear matrix inequality for magnetic bearing system which shows the control performance and robust stability under the physical parameter perturbations. To the end, the validity of the designed controller is investigated through computer simulation.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.40 no.4
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• pp.251-263
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• 2003

This paper presents matrix inequality conditions for Η$_2$control and Η$_2$controller design method of linear time-invariant descriptor systems with parameter uncertainties in continuous and discrete time cases, respectively. First, the necessary and sufficient condition for Η$_2$control and Η$_2$ controller design method are expressed in terms of LMI(linear matrix inequality) with no equality constraints in continuous time case. Next, the sufficient condition for Hi control and Η$_2$controller design method are proposed by matrix inequality approach in discrete time case. Based on these conditions, we develop the robust Η$_2$controller design method for parameter uncertain descriptor systems and give a numerical example in each case.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.5
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• pp.503-510
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• 2004

In this paper, the well-conditioned observer for a stochastic system is designed so that the observer is less sensitive to the ill-conditioning factors in transient and steady-state observer performance. These factors include not only deterministic uncertainties such as unknown initial estimation error, round-off error, modeling error and sensing bias, but also stochastic uncertainties such as disturbance and sensor noise. In deterministic perspectives, a small value in the L$_{2}$ norm condition number of the observer eigenvector matrix guarantees robust estimation performance to the deterministic uncertainties. In stochastic viewpoints, the estimation variance represents the robustness to the stochastic uncertainties and its upper bound can be minimized by reducing the observer gain and increasing the decay rate. Both deterministic and stochastic issues are considered as a weighted sum with a LMI (Linear Matrix Inequality) formulation. The gain in the well-conditioned observer is optimally chosen by the optimization technique. Simulation examples are given to evaluate the estimation performance of the proposed observer.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.67 no.5
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• pp.651-655
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• 2018

In this paper, based on an augmented Lyapunov-Krasovskii functional(LKF) with time-delay product quadratic terms, the stability result in the form of linear matrix inequality(LMI) is proposed. In getting an LMI result, the free matrix based integral inequality is used. Finally, two well-known numerical examples are given to demonstrate the usefulness of the proposed result.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.898-902
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• 2003

For linear descriptor systems, we consider the $H_{INFTY}$ controller design problem via output feedback. Both static output feedback and dynamic one are discussed. First, in the case of static output feedback, we reduce our control problem to solving a bilinear matrix inequality (BMI) with respect to the controller coefficient matrix, a Lyapunov matrix and a matrix related to the descriptor matrix. Under a matching condition between the descriptor matrix and the measured output matrix (or the control input matrix), we propose setting the Lyapunov matrix in the BMI as being block diagonal appropriately so that the BMI is reduced to LMIs. For fixed-order dynamic $H_{INFTY}$ output feedback, we formulate the control problem equivalently as the one of static output feedback design, and thus the same approach can be applied.

• Transactions on Control, Automation and Systems Engineering
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• v.2 no.1
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• pp.31-39
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• 2000

We present a robust and reliable H$\infty$ state-feedback controller design for linear uncertain systems, which have norm-bounded time-varying uncertainty in the state matrix, and their prespecified sets of actuators are susceptible to failure. These controllers should guarantee robust stability of the systems and H$\infty$ norm bound against parameter uncertainty and/or actuator failures. Based on the linear matrix inequality (LMI) approach, two state-feedback controller design methods are constructed by formulating to a set of LMIs corresponding to all failure cases or a single LMI that covers all failure cases, with an additional costraint. Effectiveness and geometrical property of these controllers are validated via several numerical examples. Furthermore, the proposed LMI frameworks can be applied to multiobjective problems with additional constraints.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.5
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• pp.806-811
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• 2017

This paper considers the delay-dependent stability of linear systems with a time-varying delay in the frame work of Lyapunov-Krasovskii functional(LKF) approach. In this approach, an integral inequality is essential to estimate the upper bound of time-derivative of LKF, and a less conservative one is needed to get a less conservative stability result. In this paper, based on free weighting matrices, an improved integral inequality encompassing well-known results is proposed and then a stability result in the form of linear matrix inequality is derived based on an augmented LKF. Finally, two well-known numerical examples are given to demonstrate the usefulness of the proposed result.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.4
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• pp.275-279
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• 2011

In this paper, an observer-based sampled-data controller of linear system is proposed for the wave energy converter. Based on the sampled-data observer, the controller is design. In the closed-loop system with controller, it obtains the norm inequality between the continuous-time state variable and the discrete-time one. Using the norm inequality, sufficient condition is derived for the asymptotic stability of the closed-loop system and formulated in terms of linear matrix inequality. Finally, the wave energy converter simulation is provided to verify the effectiveness of the proposed technique.

• Journal of Institute of Control, Robotics and Systems
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• v.11 no.1
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• pp.13-18
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• 2005

This paper considers a design problem of the repetitive control system for linear systems with time-varying norm bounded uncertainties. Using the Lyapunov functional for time-delay systems, a sufficient condition ensuring robust stability of the repetitive control system is derived in terms of an algebraic Riccati inequality (ARI) or a linear matrix inequality (LMI). Based on the derived condition, we show that the repetitive controller design problem can be reformulated as an optimization problem with an LMI constraint on the free parameter.