• 제어로봇시스템학회:학술대회논문집
• /
• 2000.10a
• /
• pp.23-23
• /
• 2000

In this paper, we proposed the problems of robust stability and 개bust H$_{\infty}$ control of discrete time-delay linear st.stems with Frobenius norm-bounded uncertainties. The existence condition and the design method of robust H$_{\infty}$ state feedback control]or are given. Through some changes of variables and Schur complement, the obtained sufficient condition can be rewritten as an LMI(linear matrix inequality) form in terms of all variables.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.58 no.1
• /
• pp.193-198
• /
• 2009

In this paper, we consider the design problem of delay-dependent robust $H{\infty}$ controller of discrete-time descriptor systems with parameter uncertainties and interval time-varying delays in state and control input by delay-dependent LMI (linear matrix inequality) technique. A new delay-dependent bounded real lemma for discrete-time descriptor systems with time-varying delays is derived. The condition for the existence of robust $H{\infty}$ controller and the robust $H{\infty}$ state feedback control law are proposed by LMI approach. A numerical example is demonstrated to show the validity of the design method.

• Journal of Institute of Control, Robotics and Systems
• /
• v.15 no.2
• /
• pp.121-127
• /
• 2009

This paper deals with the design problem of robust stabilization and non-fragile controller for discrete-time singular systems with parameter uncertainties and time-varying delays in state and input by delay-dependent Linear Matrix Inequality (LMI) approach. A new delay-dependent bounded real lemma for singular systems with time-varying delays is derived. Robust stabilization and robust non-fragile state feedback control laws are proposed, which guarantees that the resultant closed-loop system is regular, causal and stable in spite of time-varying delays, parameter uncertainties, and controller gain variations. A numerical example is given to show the validity of the design method.

• Journal of Institute of Control, Robotics and Systems
• /
• v.5 no.6
• /
• pp.641-646
• /
• 1999

This paper deals with the robust stability of discrete-time linear systems with time- varying delays and norm-bounded uncertainties. In this paper, the magnitude of time-varying delays is assumed to be upper-bounded. The sufficient condition is presented in terms of linear matrix inequality. It is also shown that the robust stability of uncertain discrete-time linear systems with time-varying delays is related with the quadratic stability of uncertain discrete-time linear systems with constant time delay.

• 제어로봇시스템학회:학술대회논문집
• /
• 1997.10a
• /
• pp.293-296
• /
• 1997

Robust stability conditions for discrete-time variable structure control is proposed. Conventionally the discrete-time variable structure control method with a variable structure uncertainty compensator approach requires a bounded changing rate of the uncertainties to ensure robust stability. However, when uncertainties vary as a function of state variables, which occur with parametric uncertainties, it is not reasonable to assume a bounded variation on the uncertainties. In this paper, uncertainties are assumed to consist of exogenous disturbances and parametric uncertainties. An uncertainty compensator is used to deal with the former, and a robust stability condition is derived using Small Gain Theorem for the latter.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.20 no.11
• /
• pp.3560-3572
• /
• 1996

This paper presents a new discrete-time fuzzy-sliding mode controller for robust vibration control of a smart structure featuring a piezofilm actuator. A governong equation of motion for the smart beam structure is derived and discrete-time codel with mismatched uncertainties such as parameter variations is constructed ina state space. A discrete-time sliding mode control system consisting of an equivalent controller and a discontinuous controller is formulated. In the design of the equivalent part, so called an equivalent controller separation method is adopted to achieve vzster convergence to a sliding surface without extension of a sliding region, in which the system robustness maynot be guaranteed. On the other hand, the discontinuous part is constructed on the basis of both the sliding and the convergence conditions using a time-varying feedback gain. The sliding moide controller is then incorporated with a fuzzy technique to appropriately determine principal control parameters such as a discountinuous feedback gain. Experimental implementation on the forced and random vibraiton controls is undertaken in order to demonstrate superior control performance of the proposed controller.

• 제어로봇시스템학회:학술대회논문집
• /
• 2003.10a
• /
• pp.322-326
• /
• 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.

• Journal of the Institute of Electronics Engineers of Korea SC
• /
• v.46 no.3
• /
• pp.15-21
• /
• 2009

In this paper, we consider the design problem of robust stabilization and robust guaranteed cost state feedback controller for discrete-time singular systems with parameter uncertainties by LMI(linear matrix inequality) approach without semi-definite condition and decomposition of system matrices. The objective of robust stabilization controller is to construct a state feedback controller such that the closed-loop system is regular, causal, and stable. In the case of robust guaranteed cost control, the optimal value of guaranteed cost and controller design method are presented on the basis of robust stabilization control technique. Finally, a numerical example is provided to show the validity of the design methods.

• 제어로봇시스템학회:학술대회논문집
• /
• 1996.10a
• /
• pp.303-306
• /
• 1996

We propose a robust tuning method of the quadratic criterion based iterative learning control(Q-ILC) algorithm for discrete-time linear batch system. First, we establish the frequency domain representation for batch systems. Next, a robust convergence condition is derived in the frequency domain. Based on this condition, we propose to optimize the weighting matrices such that the upper bound of the robustness measure is minimized. Through numerical simulation, it is shown that the designed learning filter restores robustness under significant model uncertainty.

• Journal of Institute of Control, Robotics and Systems
• /
• v.2 no.3
• /
• pp.158-164
• /
• 1996

In this paper, we consider the problem of robust stability of discretd time-delay systems subjected to perturbations. Two classes of perturbations are treated. The first one is the nonlinear norm-bounded perturbation, and the second is the structured time-varying parametric perturbation. Based on the discrete-time Lyapunov stability theory, several new sufficient conditions for robust stability of the system are presented. From these conditions, we can estimate the maximum allowable bounds of the perturbations which guarantee the stability. Finally, numerical examples are given to demonstrate the effectiveness of the results.