• Proceedings of the KIEE Conference
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• 1997.07b
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• pp.620-623
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• 1997

This paper is concerned with the design of a suboptimal Kalman filter with robust state estimation performance for system models represented in the state space, which are subjected to parameter uncertainties in both the state and measurement matrices. Under the assumption that the uncertain system is quadratically stable, if the augmented system composed of the uncertain system and the filter is controllable, the proposed filter can provide the upper bound of the estimation error variance for all admissible uncertain parameters. This upper bound can be represented as the convex function of a parameter introduced in the design procedure, and the optimized upper bound of the estimation error variance can also be found via the optimization of this convex function.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.05a
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• pp.321-324
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• 2003

This paper discusses a robust stochastic stabilization of uncertain Takagi-Sugeno (T-S) fuzzy system with Markovian input delay. The finite Markovian process is adopted to model the input delay of the overall control system. It is assumed that the zero and hold devices are used for control input. The continuous-time T-S fuzzy system with the Markovian input delay is discretized for easy handling delay, accordingly, the discretixzd T-S fuzzy system is represented by a uncertain discrete-time T-S fuzy system with jumping parameters. The robust stochastic stabilizibility of the uncertain jump T-S fuzzy system is derived and formulated in terms of linear matrix inequalities (LMIs).

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.48 no.6
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• pp.8-14
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• 2011

In this note, a proof of Utkin's theorem is presented for SI(Single input) uncertain linear systems. The invariance theorem with respect to the two transformation methods so called the two diagonalization methods is proved clearly and comparatively for SI uncertain linear systems. With respect to the sliding surface transformation, the equation of the sliding mode i.e., the sliding surface is invariant. The control inputs by the two transformation methods both have the same gains. By means of the two transformation methods, the same results can be obtained. Through an illustrative example and simulation study, the usefulness of the main results is verified.

• International Journal of Naval Architecture and Ocean Engineering
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• v.11 no.1
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• pp.606-623
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• 2019

The path following problem of a ship sailing in restricted waters under wind effect is investigated based on Robust $H_{\infty}$ Guaranteed Cost Control (RHGCC). To design the controller, the ship maneuvering motion is modeled as a linear uncertain system with norm-bounded time-varying parametric uncertainty. To counteract the bank and wind effects, the integral of path error is augmented to the original system. Based on the extended linear uncertain system, sufficient conditions for existence of the RHGCC are given. To obtain an optimal robust $H_{\infty}$ guaranteed cost control law, a convex optimization problem with Linear Matrix Inequality (LMI) constraints is formulated, which minimizes the guaranteed cost of the close-loop system and mitigates the effect of external disturbance on the performance output. Numerical simulations have confirmed the effectiveness and robustness of the proposed control strategy for the path following goal of a ship sailing in restricted waters under wind effect.

• Journal of Institute of Control, Robotics and Systems
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• v.13 no.10
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• pp.1000-1006
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• 2007

This paper presents an LMI-based method to design a saturated state-feedback $H_2$ controller for uncertain systems with actuator saturation. Specifically, the paper proposes a sufficient condition such that the system under norm-bounded uncertainties and actuator saturation is asymptotically stable and the $H_2$-norm of the system has an upper-bound. The resulting condition is further utilized to solve a convex optimization problem specified in the context of $H_2$-norm minimization, whose solution yields a saturated $H_2$ controller. A numerical example is presented to show the effectiveness of the proposed method.

• Proceedings of the KIEE Conference
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• 2006.07d
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• pp.1854-1855
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• 2006

In this paper, the Takagi-Sugeno (TS) fuzzy state estimation scheme, which is suggested for a steady state estimator using standard Kalman filter theory with uncertainties. In that case, the steady state with uncertain can be represented by the TS fuzzy model structure, which is further rearranged to give a set of uncertain linear model using standard Kalman filter theory. And then the unknown uncertainty is regarded as an additive process noise. To optimize fuzzy system, we utilize the genetic algorithm. The steady state solutions can be found for proposed linear model then the linear combination is used to derive a global model. The proposed state estimator is demonstrated on a truck-trailer.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.62 no.5
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• pp.679-687
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• 2013

This paper proposes a new condition about delay-dependent robust $H_{\infty}$ control of uncertain linear systems with time-varying delay and randomly occurring disturbances. The norm bounded uncertainties are subjected to the system matrices. Based on Lyapunov stability theory, a sufficient condition for designing a controller gain such that the closed-loop systems are asymptotically stable with $H_{\infty}$ disturbance level ${\gamma}$ is formulated in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are included to show the effectiveness of the presented method.

• Coupled systems mechanics
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• v.1 no.4
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• pp.345-360
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• 2012

In this article we have presented a unique representation for interval arithmetic. The traditional interval arithmetic is transformed into crisp by symbolic parameterization. Then the proposed interval arithmetic is extended for fuzzy numbers and this fuzzy arithmetic is used as a tool for uncertain finite element method. In general, the fuzzy finite element converts the governing differential equations into fuzzy algebraic equations. Fuzzy algebraic equations either give a fuzzy eigenvalue problem or a fuzzy system of linear equations. The proposed methods have been used to solve a test problem namely heat conduction problem along with fuzzy finite element method to see the efficacy and powerfulness of the methodology. As such a coupled set of fuzzy linear equations are obtained. These coupled fuzzy linear equations have been solved by two techniques such as by fuzzy iteration method and fuzzy eigenvalue method. Obtained results are compared and it has seen that the proposed methods are reliable and may be applicable to other heat conduction problems too.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.39 no.7
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• pp.729-739
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• 1990

This paper deals with the fault detection problem in uncertain linear/non-linear systems having both undermodelling and noise. A robust fault detection method is presented which accounts for the effects of noise, model mismatch and nonlinearities. The basic idea is to embed the unmodelled dynamics in a stochastic process and to use the nominal model with a predetermined fixed denominator. This allows the input /output relationship to be represented as a linear function of the system parameters and also facilitate the quatification of the effect of noise, model mismatch and linearization errors on parameter estimation by the Bayesian method. Comparisons are made via simulations with traditional fault detection methods which do not account for model mismatch or linearization errors. The new method suggested in this paper is shown to have a marked improvement over traditional methods on a number of simulations, which is a consequence of the fact that the new method explicitly for the effects of undermodelling and linearization errors.

• Structural Engineering and Mechanics
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• v.29 no.5
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• pp.489-504
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• 2008

In piezoelectric flexible structures, the contribution of vibration modes to the dynamic response of system may change with the location of piezoelectric actuator patches, which means that the ability of actuators to control vibration modes should be taken into account in the development of modal reduction model. The spatial $H_2$ norm of modes, which serves as a measure of the intensity of modes to system dynamical response, is used to pick up the modes included in the reduction model. Based on the reduction model, the paper develops the state-space representation for uncertain flexible tructures with piezoelectric material as non-collocated actuators/sensors in the modal space, taking into account uncertainties due to modal parameters variation and unmodeled residual modes. In order to suppress the vibration of the structure, a dynamic output feedback control law is designed by imultaneously considering the conflicting performance specifications, such as robust stability, transient response requirement, disturbance rejection, actuator saturation constraints. Based on linear matrix inequality, the vibration control design is converted into a linear convex optimization problem. The simulation results show how the influence of vibration modes on the dynamical response of structure varies with the location of piezoelectric actuators, why the uncertainties should be considered in the reductiom model to avoid exciting high-frequency modes in the non-collcated vibration control, and the possiblity that the conflicting performance specifications are dealt with simultaneously.