• 제어로봇시스템학회논문지
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• 제9권11호
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• pp.861-867
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• 2003

We propose a sliding surface design method for linear systems with mismatched uncertainties in the state space model. In terms of LMIs, we derive a necessary and sufficient condition for the existence of a linear sliding surface such that the reduced-order equivalent sliding mode dynamics restricted to the linear sliding surface is not only stable but completely invariant to mismatched uncertainties. We give an explicit formula of all such linear switching surfaces in terms of solution matrices to the LMI existence condition. We also give a switching feedback control law, together with a design algorithm. Additionally, we give some hints for designing linear switching surfaces guaranteeing pole clustering constraints or linear quadratic performance bound constraints. Finally, we give a design example in order to show the effectiveness of the proposed methodology.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2004년도 ICCAS
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• pp.672-677
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• 2004

In this paper, a new dual-rate digital control technique for the Takagi-Sugeno (T-S) fuzzy system is suggested. The proposed method takes account of the stabilizablity of the discrete-time T-S fuzzy system at the fast-rate sampling points. Our main idea is to utilize the lifted control input. The proposed approach is to obtain the dual-rate discrete-time T-S fuzzy system by discretizing the overall dynamics of the T-S fuzzy system with the lifted control, and then to derive the sufficient conditions for the stabilization in the sense of the Lyapunov asymptotic stability for this system. An example is provided for showing the feasibility of the proposed discretization method.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2003년도 ICCAS
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• pp.892-897
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• 2003

This paper considers the design of mixed $H_2/\;H_{\infty}$ controllers for linear time-invariant descriptor systems. Firstly, an $H_{\infty}$ and $H_2$ synthesis problem for a descriptor system are presented separately in terms of linear matrix inequalities (LMIs) based on the bounded real lemma. Then, the existence of a mixed $H_2/\;H_{\infty}$ controller by which the $H_2$ norm of the second channel is minimized while keeping the $H_{\infty}$ norm bound of the first channel less than ${\gamma}$, is reduced to the linear objective minimization problem. The class of desired controllers that are assumed to have the same structure as the plant is parameterized by using the linearizing change of variables. In addition, we show the procedure by which a obtained descriptor controller can be transformed to a non-descriptor one.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2003년도 ICCAS
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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.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2003년도 ICCAS
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• pp.322-326
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• 2003

In this paper, we establish a new robust $H_{\infty}$ performance condition for uncertain discrete-time systems with convex polytopic uncertainties. We express the condition as a set of linear matrix inequalities (LMIs), which are used to check stability and $H_{\infty}$ disturbance attenuation level by a parameter-dependent Lyapunov matrix. We show that the new condition provides less conservative result than the existing ones which use single Lyapunov matrix. We also show that the robust $H_{\infty}$ state feedback design problem for such uncertain discrete-time systems can be easily dealt with using the approach. The key point in this paper is to propose a kind of decoupling between the Lyapunov matrix and the system matrices in the parameter-dependent matrix inequality by introducing one new matrix variable.

• 제어로봇시스템학회논문지
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• 제10권7호
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• pp.618-624
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• 2004

This paper presents a delay dependent fuzzy H_\infty$ filter design method for delayed fuzzy dynamic systems. Using delay-dependent Lyapunov function, the global exponential stability and H_\infty$ performance problem are discussed. A sufficient condition for the existence of fuzzy filter is presented in terms of linear matrix inequalities(LMIs). The filter design utilize the concept of parallel distributed compensation. And the filter gains can also be directly obtained from the LMI solutions. A simulation example is given to illustrate the design procedures and performance of the proposed methods.

• 제어로봇시스템학회논문지
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• 제17권7호
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• pp.625-628
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• 2011

This paper presents an LMI-based method to design an integral sliding mode controller for a class of uncertain systems with unmatched uncertainties. The uncertain system under consideration may have unmatched parameter uncertainties in the state matrix as well as in the input matrix. Using LMIs an existence condition of a sliding surface is derived. And a switching feedback control law is given. Finally, numerical examples are given to show that the proposed method can be better than the existing results for some cases.

• 제어로봇시스템학회논문지
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• 제15권3호
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• pp.255-257
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• 2009

The robust stabilization problem of a multivariable uncertain system with a polytopic model is considered. A PI-type $H_{\infty}$ controller with a low pass filter is used for robust stabilization and noise rejection. The problem is reduced to an LMI optimization problem. A sufficient condition for the existence of the PI controller is derived in terms of LMIs. The PI gain matrices are parameterized by using the solution matrices to the existence conditions. Finally, a numerical design example is given.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2003년도 하계종합학술대회 논문집 V
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• pp.2589-2592
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• 2003

In this paper, a robust mixed H$_2$/H$\_$$\infty$/ output feedback control method is applied to the design of loop filter for PLL carrier phase tracking. The proposed method successfully copes with large S-curve slope uncertainty and a significant decision delay in the closed-loop that may exist In modern receivers due to a convolutional decoder or an equalizer. The objective is to design an output feedback controller which minimizes the H$_2$performance while satisfying the H$\_$$\infty$/ performance to guarantee the gain margin and phase margin for linear time invariant(LTI) polytopic uncertain systems. LMIs based approach is given to solve this problem. We can verify the H$\_$$\infty$/ performance satisfaction and minimize the phase detector error through the simulation result.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2004년도 학술대회 논문집 정보 및 제어부문
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• pp.110-113
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• 2004

A delay dependent fuzzy $H_{\infty}$ controller design method for delayed nonlinear systems with parameter uncertainty is considered. Using delay-dependent Lyapunov function the asymptotical stability and $H_{\infty}$n performance problem :are discussed. A sufficient condition for the existence of fuzzy controller is presented in terms of linear matrix inequalities(LMIs). A simulation example through radar gimbal system is given to illustrate the design procedures and performances of the prosed methods.