Min Kook Song

Robust stabilization for uncertain Markovian jump fuzzy systems based on free weighting matrix method

This paper presents a new methodology of robust state feedback fuzzy controller based on free weighting matrix method for a class of uncertain Markovian jump nonlinear systems. The class of systems under consideration is represented by the T-S fuzzy model with partly known transition probability matrix. The free weighting matrix method is proposed to obtain a less conservative stochastic stability criterion of the uncertain Markovian jump fuzzy systems (MJFSs) in terms of linear matrix inequalities (LMIs). Furthermore, a sufficient condition for the mode-dependent state feedback fuzzy controller is derived for the MJFSs for all admissible parameter uncertainties. Finally, a simulation example is provided to illustrate the effectiveness of the proposed methodology.

Delay-range dependent stability analysis for T-S fuzzy systems with time-varying delay

This paper is concerned with the stability analysis of Takagi-Sugeno (T-S) fuzzy systems with time varying delays by using novel quadratic Lyapunov-Krasovskii functionals. The novel Lyapunov-Krasovskii functionals comes from some existing ones employed in the previous results and add another part which is constructed by dividing the delay range into several segments and choosing proper functionals with free weighted matrices corresponding to different segments. Then using these delay partitioning idea, some new delay-range-dependent stability criteria are derived for T-S fuzzy systems. All the sufficient conditions are established in terms of linear matrix inequalities (LMIs), which can be solved efficiently by using the LMI algorithm. It is shown that these criteria for T-S fuzzy systems with time varying delays are always less conservative than the previous results. Two numerical examples are given to illustrate the less conservatism of the proposed method.

Delay-dependent observer-based control for a class of neutral systems with uncertain delays

In this paper, the observer-based control for a class of linear neutral systems is considered. The analysis is based on the use of Lyapunov-Krasovskii functional stability theory. Delay-dependent stabilization criteria are proposed to guarantee stability for the systems. The linear matrix inequalities (LMIs) approach is used to design the observer and the feedback control. A numerical example is given to illustrate the use of our main results.

Delay-range-dependent Stability Analysis and Stabilization for Nonlinear Systems : T-S Fuzzy Model Approach

This paper concerns delay-range-dependent robust stability and stabilization for time-delay nonliner system via T-S fuzzy model approach. The time delay is assumed to be a time-varying continuous function belonging to a given range. On the basis of a novel Lyapunov-Krasovskii functional, which includes the information of the range, delay-range-dependent stability criteria are established in terms of linear matrix inequality. It is shown that the new criteria can provide less conservative results than some existing ones. Moreover, the stability criteria are also used to design the stabilizing state-feedback controllers. Numerical examples are given to demonstrate the applicability of the proposed approach.

Delay range dependent fuzzy control design for nonlinear neutral systems with time varying delays

In this paper, a new type of Lyapunov--Krasovskii functional method is constructed to study delay-range-dependent stability analysis and stabilization problems for Takagi--Sugeno T--S fuzzy neutral systems with time-varying delay. The present results may improve the existing ones due to a method to estimate the upper bound of the derivative of Lyapunov-Krasovskii functional without ignoring some useful terms and the introduction of additional terms into the proposed Lyapunov-Krasovskii functional, which take into account the range of delay. On the basis of a novel Lyapunov--Krasovskii functionals, which includes the information of the range of dealy, delay-range-dependent stability criteria are established in terms of linear matrix inequalities LMIs. Moreover, the stability criteria are also used to design a stabilizing fuzzy controller. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.

Further Results on Stability and Stabilization of T{S Fuzzy Neutral Systems with Time-Varying Delays Using Delay Dividing Approach

This paper is concerned with the stability and the stabilization problem for Takagi–Sugeno (T–S) fuzzy systems with neutral time delays. The sufficient stability conditions are derived using novel Lyapunov–Krasovskii functionals (LKFs). The stability conditions are expressed as linear matrix inequalities (LMIs) and hence easily tractable numerically. These conditions are easily extended to the sufficient conditions for the existence of stabilizing state-feedback fuzzy gains for T–S fuzzy neutral systems with time-varying delays. An example is given to illustrate the effectiveness of the proposed methods.

Output-feedback stabilization for fuzzy descriptor systems with neutral time delays

This paper investigates the stability and stabilization problem for nonlinear systems with neutral time delays represented by the Takagi-Sugeno (T-S) fuzzy model. First, the T-S fuzzy models with neutral time-delay are present and the stability conditions are derived in form of linear matrix inequalities (LMIs). Then a stabilization approach for nonlinear neutral systems through fuzzy output feedback controller is proposed. It shows that the analysis results provide an efficient technique for the design for fuzzy output feedback controllers. Sufficient conditions for the existence of fuzzy output feedback gain of the neutral time-delay systems are derived through the numerical solution of derived LMIs.

Stability analysis and synthesis of Markovian jump nonlinear systems with incomplete transition descriptions via fuzzy control

This paper is concerned with exploring an extended approach for the stability analysis and synthesis for Markovian jump nonlinear systems (MJNLSs) with incomplete transition descriptions via fuzzy control. In this paper, not all the elements of the rate transition matrices (RTMs) are assumed to be known. By fully considering the properties of the RTMs and the convexity of the uncertain domains, sufficient criteria of stability and stabilization are obtained. The proposed stability conditions are much less conservative than most of the existing results and stabilization conditions with a mode-dependent fuzzy controller are derived for Markovian jump fuzzy systems (MJFSs) in terms of linear matrix inequalities (LMIs). Finally, illustrative numerical examples are provided to demonstrate the effectiveness of the proposed approach.

Time-delayed feedback control of chaotic T-S fuzzy systems

This paper deals with the time-delayed feedback control of periodic orbits in the chaotic T-S fuzzy systems. A chaotic system has embedded within it an infinite number of unstable periodic orbits (UPOs). Tracking UPOs is of particular interest in chaos-control research. A novel and efficient idea is to control by means of time-delayed feedback control (TDFC). Recently, a number of analytic T-S fuzzy systems for the chaotic systems have been found. Thus it is interesting to design a controller under the framework of TDFC. A analytic sufficient condition for the chaotic T-S fuzzy systems from the TDFC approach is derived in terms of linear matrix inequalities (LMIs). A gradient-decent based adaptation algorithm is incorporated with the fuzzy-model-based TDFC to estimate the period of the UPO. The established theoretical results are clarified by the numerical example.

Stability Analysis and Stabilization for Neutral Networked Control System

Abstract This paper focuses on the stability analysis and stabilization for networked control system with neutral type of time-delay. By utilizing the delay partitioning idea, new stabi lity criteria are proposed in terms of linear matrix inequalities(LMIs). These conditions are developed based on the Lyapunov-Krasovskii functionals. Based on the derived criteria, a sufficient condition for te solvability of this problem is obtained in terms of linear matrix inequality without decomposing the original system matrices. Also, it is s hown that the proposed controller design method is general for networked control systems. Finally, illustrative ex amples are presented to show the applicability of the proposed method. Key Words : Fuzzy controller, linear matrix inequality, networked control system, time-delay 1. 서 론 흔히 플랜트, 센서, 제어기 그리고 구동기가 네트워크상의 폐루프의 구조로 이루어진 시스템을 네트워크 제어 시스템이라고 한다. 이러한 네트워크 제어 시스템에는 시스템의 특징상 시간 지연 현상 및 데이터 손실이 발견된다. 이러한 시간 지연 및 데이터 손실을 포함한 네트워크 제어 시스템은 시간지연에 의해 시스템의 성능이 떨어지고, 심지어는 시스템이 불안정해 질수도 있다. 따라서 이러한 시간 지연현상이 반드시 포함되는 네트워크 시스템의 안정도 해석에 관한 연구가 주요 관심사가 되어 왔으며, 활발한 연구가 진행되어 왔다 [1-6].그러나 지금까지 연구된 대부분의 네트워크 제어 시스템은 상태 변수나 입력의 시간지연에만 국한되어 왔다 [2-6]. 시스템에서 상태변수 뿐 아니라 상태 변수의 1차 미분 항에도 시간 지연 현상이 발견되고 있으며 이러한 시스템이 모델링되고 있다. 상태 변수 뿐 아니라 1차 미분항에도 시간 지연을 가지는 시스템을 뉴트럴 시스템이라고 한다. 지금까지의 연구는 뉴트럴 타입시간 지연 현상에 대해서 연구되어오지 않았으며, 더군다나 네트워크 제어 시스템 분야에서는 뉴트럴 타입 시간 지연에 대한 모델링도 이루어지고 있지 않다. 따라서 본 논문에서는 뉴트럴 타입 시간 지연을 포함하는 네트워크 제어 시스템의 안정도 분석 및 제어기 설계를 연구하였다.본 논문에서는 시간 지연 분산 설계 기법을 이용하여 뉴트럴 타입 시간 지연을 가지는 네트워크 시스템 시스템의