• 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 CI
• /
• v.40 no.6
• /
• pp.69-75
• /
• 2003

This paper presents a fuzzy logic based approach to tracking control of a sampled nonlinear system. It is assumed that the plant to be controlled is under both the internal uncertainty and the external disturbances. Discrete-time adaptive fuzzy control method is proposed and its parameters are determined by the recently-spolighted convex optimization technique called LMI. Finally, the computer simulation is tarried out to verify the effectiveness of the proposed method.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.63 no.7
• /
• pp.994-1000
• /
• 2014

This paper considers the problem of continuous and discrete time dissipative filter design method for the singular systems with polytopic uncertainties. Two bounded real lemmas (BRL) for the robust filters of dissipative singular systems along with the polytopic uncertainties are proposed on the basis of Lyapunov criterion. The sufficient conditions for both continuous and discrete time dissipative filter design methods are derived using the obtained BRL by linear matrix inequality (LMI) approach. Finally, the validities of the proposed methods are shown by numerical examples.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.64 no.6
• /
• pp.891-899
• /
• 2015

This paper presents the robust stability condition of uncertain Takagi-Sugeno(T-S) fuzzy systems with time-varying delay. New augmented Lyapunov-Krasovskii function is constructed to ensure that the system with time-varying delay is globally asymptotically stable. Also, less conservative delay-dependent stability criteria are obtained by employing some integral inequality, reciprocally convex approach and new delay-partitioning method. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed method.

• Proceedings of the KIEE Conference
• /
• 2009.07a
• /
• pp.1724_1725
• /
• 2009

In this paper, new approaches to optimal controller design for a class of discrete-time Takagi-Sugeno (T-S) fuzzy systems are proposed based on a relaxed approach, in which non-quadratic Lyapunov function and non-parallel distributed compensation (PDC) control law are used. New relaxed conditions and linear matrix inequality (LMI) based design methods are proposed that allow outperforming previous results found in the literature. Finally, an example is given to demonstrate the efficiency of the proposed approaches.

• Journal of the Korean Mathematical Society
• /
• v.48 no.4
• /
• pp.775-795
• /
• 2011

The disturbance attenuation problem for a class of discretetime switched linear systems with exponential uncertainties via switched state feedback and switched dynamic output feedback is investigated, respectively. By using Taylor series approximation and convex polytope technique, exponentially uncertain discrete-time switched linear system is transformed into an equivalent switched polytopic model with additive norm bounded uncertainty. For such equivalent switched model, one designs its switching strategy and associated state feedback controllers and dynamic output feedback controllers so that whole switched model is asymptotical stabilization with H-in nity disturbance attenuation base on switched Lyapunov function and LMI approach. Finally, two numerical examples are presented to illustrate our results.

• Proceedings of the KIEE Conference
• /
• 2005.07d
• /
• pp.2815-2817
• /
• 2005

This paper presents an experiment study on the control of a rotary-type inverted pendulum based on the Takagi-Sugeno (T-S) fuzzy model approach. A sufficient condition for stability of the T-S fuzzy control system is given via linear matrix inequalities (LMIs). State-feedback controllers for sub-systems are designed from the sufficient condition via change of variables which is one of the popular LMI techniques. Experimental results on a rotary-type inverted pendulum control show the feasibility of the T-S fuzzy model-based control method.

• 제어로봇시스템학회:학술대회논문집
• /
• 2005.06a
• /
• pp.1492-1495
• /
• 2005

This paper presents a new linear-matrix-inequality-based intelligent digital redesign (LMI-based IDR) technique to match the states of the analog and the digital T-S fuzzy control systems at the intersampling instants as well as the sampling ones. The main features of the proposed technique are: 1) the affine control scheme is employed to increase the degree of freedom; 2) the fuzzy-model-based periodic control is employed; and the control input is changed n times during one sampling period; 3) The proposed IDR technique is based on the approximately discretized version of the T-S fuzzy system; but its discretization error vanishes as n approaches the infinity. 4) some sufficient conditions involved in the state matching and the stability of the closed-loop discrete-time system can be formulated in the LMIs format.

• Journal of Institute of Control, Robotics and Systems
• /
• v.14 no.7
• /
• pp.615-623
• /
• 2008

This paper proposes an $H_{\infty}$ controller design method for Takagi-Sugeno (T-S) fuzzy systems using a fuzzy basis-function-dependent Lyapunov function. Sufficient conditions for the guaranteed $H_{\infty}$ performance of the T-S fuzzy control system are given in terms of linear matrix inequalities (LMIs). These LMI conditions are further used for a convex optimization problem in which the $H_{\infty}-norm$ of the closed-loop system is to be minimized. To facilitate the basis-function-dependent Lyapunov function approach and thus improve the closed-loop system performance, additional decision variables are introduced in the optimization problem, which provide an additional degree-of-freedom and thus can enlarge the solution space of the problem. Numerical examples show the effectiveness of the proposed method.

• Proceedings of the IEEK Conference
• /
• 1998.06a
• /
• pp.227-230
• /
• 1998

In this paper, we propose the design method of fuzzy robust H$\infty$ controller for the uncertain nonlinear discete-time systems with time delay. First, we represent a nonlinear plant with a modified T-S(Takagi-Sugeno) fuzzy model. Then design method utilizing the concept of PDC (parallel distributed compensation) is employed. For the modified T-S fuzzy model with uncertainty and delay, the sufficient condition of the quadratic stabilization with an H$\infty$ norm bound is presented in terms of Lyapunov stability theory and fuzzy robust H$\infty$ controller design method is given by LMI(linear matrix inequality) approach. Also an illustrative example is given to demonstrate the result of the proposed method.