Observer-based control of positive polynomial fuzzy systems with unknown time delay

Published on Jul 1, 2019in Neurocomputing4.072
· DOI :10.1016/j.neucom.2019.04.016
Meng Han (Yanshan University), Hak-Keung Lam46
Estimated H-index: 46
('KCL': King's College London)
+ 2 AuthorsChangzhu Zhang5
Estimated H-index: 5
(Tongji University)
Abstract This paper presents a methodology to investigate the observer-based control for positive nonlinear systems with unknown time delay through analyzing the stability and positivity of positive polynomial fuzzy-model-based (PPFMB) observer-control systems with unknown time delay and unmeasurable premise variables. In order to widen the application of research results and relax the research results, the polynomial fuzzy observer-controller employs a membership function depending on estimated premise variables and the observer system matrix is treated as decision variable. This scenario will lead to non-convex stability and positivity conditions when the stability and positivity are analyzed based on the Lyapunov stability theory. To overcome this issue, some transformation techniques and matrix decoupling techniques (MDT) are adopted to turn the non-convex stability/positivity conditions into convex ones so that they can be handled by convex programming techniques. Finally, two simulation examples are presented to demonstrate the feasibility and validity of the analysis results.
  • References (49)
  • Citations (0)
📖 Papers frequently viewed together
2014CDC: Conference on Decision and Control
4 Authors (Ali Chibani, ..., N. Benhadj Braiek)
1 Citations
6 Citations
2 Citations
78% of Scinapse members use related papers. After signing in, all features are FREE.
#1Likui Wang (Nanchang Hangkong University)H-Index: 3
#2Hak-Keung Lam ('KCL': King's College London)H-Index: 46
In this technical paper, a new Lyapunov–Krasovskii functional (LKF) is designed to study the stability of continuous-time Takagi–Sugeno fuzzy systems with time-varying delay. The integrand of the LKF depends on integral variable and time {t}which can help to reduce the number of linear matrix inequalities (LMIs). Then, a new stability criterion is derived by analyzing the sign of the time derivatives of membership functions. Compared with the existing results, larger delay bounds can be obtai...
10 CitationsSource
Feb 1, 2019 in SMC (Systems, Man and Cybernetics)
#1Hui Ma (Bohai University)H-Index: 6
#2Qi Zhou (Bohai University)H-Index: 24
Last. Hongjing Liang (Bohai University)H-Index: 13
view all 4 authors...
This paper is focused on the observer-based adaptive fuzzy control problem for nonlinear stochastic systems with the nonstrict-feedback form, in which some complicated and challenging issues including unmeasurable states, input quantization and actuator faults are addressed. The fuzzy logic systems are introduced to approximate the nonlinear functions existing in the control system. A fuzzy observer is designed to observe the unavailable state variables. In order to handle the negative effects r...
30 CitationsSource
#1Xin Zhao (Qingdao University)H-Index: 1
#2Chong Lin (Qingdao University)H-Index: 40
Last. Qing-Guo Wang (UJ: University of Johannesburg)H-Index: 8
view all 4 authors...
Abstract This paper is concerned with the problem of the stability and stabilization for continuous-time Takagi–Sugeno(T–S) fuzzy systems with time delay. A novel Lyapunov–Krasovskii functional which includes fuzzy line-integral Lyapunov functional and membership-function-dependent Lyapunov functional is proposed to investigate stability and stabilization of T–S fuzzy systems with time delay. In addition, switching idea which can avoid time derivative of membership functions is introduced to dea...
9 CitationsSource
#1Likui Wang (Nanchang Hangkong University)H-Index: 3
#2Hak-Keung Lam ('KCL': King's College London)H-Index: 46
Till now, there are lots of stability and stabilization results about Takagi–Sugeno (T–S) fuzzy systems with time delay, but most of them are independent of the analysis of membership functions. Since the membership functions are an essential component to make a fuzzy system different from others, the conditions without its information are conservative. In this brief paper, a new Lyapunov–Krasovskii functional is designed to investigate the stability and stabilization of continuous-time T–S fuzz...
29 CitationsSource
#1Ali Chibani (Carthage University)H-Index: 4
#2Mohammed Chadli (University of Picardie Jules Verne)H-Index: 38
Last. Naceur Benhadj Braiek (Carthage University)H-Index: 14
view all 4 authors...
Abstract This paper investigates the problem of fault detection filter design for discrete-time polynomial fuzzy systems with faults and unknown disturbances. The frequency ranges of the faults and the disturbances are assumed to be known beforehand and to reside in low, middle or high frequency ranges. Thus, the proposed filter is designed in the finite frequency range to overcome the conservatism generated by those designed in the full frequency domain. Being of polynomial fuzzy structure, the...
13 CitationsSource
#1Linlin Li (USTB: University of Science and Technology Beijing)H-Index: 11
#2Mohammed Chadli (University of Duisburg-Essen)H-Index: 38
Last. Ying Yang (PKU: Peking University)H-Index: 16
view all 5 authors...
This paper deals with a real-time-weighted observer-based fault-detection (FD) scheme for Takagi–Sugeno (T–S) fuzzy systems. The essential idea is to develop a weighted diagnostic observer-based FD system to optimize the worst case robustness and fault sensitivity simultaneously by using the information provided by each local system. To achieve an early detection of potential fault, the robustness issue is investigated in the \mathcal {L}_{\infty }/\mathcal {L}_2observer-based FD context. Mea...
52 CitationsSource
#1Likui Wang (Nanchang Hangkong University)H-Index: 3
#2Hak-Keung Lam ('KCL': King's College London)H-Index: 46
This brief paper investigates the local stabilization for continues-time Takagi–Sugeno fuzzy systems with constant time delay. In order to deal with the time delay, we design a Lyapunov–Krasovskii functional that is dependent on the membership function. Based on the Lyapunov–Krasovskii functional and the analysis of the time derivative of the membership function, less conservative results can be obtained; however, the Lyapunov–Krasovskii functional is designed so complicated that the Lyapunov le...
28 CitationsSource
#1Likui Wang (Nanchang Hangkong University)H-Index: 1
#2Juanjuan Liu (Nanchang Hangkong University)H-Index: 1
Abstract In this brief paper, a membership function dependent Lyapunov–Krasovskii functional is designed to investigate the stability analysis of T–S (Takagi–Sugeno) fuzzy systems with time delay. According to the time derivatives of the membership function, both local and global stability conditions are obtained. For the local case, the local stability region is obtained by designing an algorithm. In the end, an example is given to illustrate the effectiveness of the method in this paper.
4 CitationsSource
This paper reviews the stability analysis of continuous-time fuzzy-model-based (FMB) control systems, with emphasis on state-feedback control techniques, which is an essential issue received a great deal of attention in the fuzzy control community. It gives an overview of the milestones and the trend of developments and achievements for the past decades. Focusing on the stability analysis of FMB control systems, it summarizes the issues in the four fundamental and essential aspects, namely, the ...
24 CitationsSource
#1Shengli Du (Beijing University of Technology)H-Index: 1
#2Junfei Qiao (Beijing University of Technology)H-Index: 21
Abstract This paper is concerned with the stability analysis and L1-gain controller synthesis problem of continuous-time switched positive T–S fuzzy systems with time-varying delays. Some sufficient conditions guaranteeing the stability and a desired L1-gain performance of an autonomous switched positive T–S fuzzy system are first presented. The sufficient conditions are developed by adopting the mode-dependent average dwell time (MDADT) technique. Then, fuzzy controllers of two classes of switc...
6 CitationsSource
Cited By0