The Lyapunov approach to the stability analysis of discrete singular systems

This paper focuses on the development of a stable Mamdani type-2 fuzzy logic based controller for automatic control of servo systems. The stability analysis of the fuzzy controller has been done by employing the concept of Lyapunov. The Lyapunov approach results in the derivation of an original stability analysis that can be used for designing the rule base of our proposed online gain adaptive Interval Type-2 Fuzzy Proportional Derivative controller (IT2-GFPD) for servo systems with assured stability. In this approach a Quadratic positive definite Lyapunov function is used and sufficient stability conditions are satisfied by the adaptive type-2 fuzzy logic control system. Illustrative simulation studies with linear and nonlinear models as well as experimental results on a real-time servo system validate the stability and robustness of the developed intelligent IT2-GFPD. A comparative performance study of IT2-GFPD with other controllers in presence of noise and disturbance also proves the superiority of the proposed controller.

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Robust D-stability analysis for uncertain discrete singular systems with state delay

IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications ◽

10.1109/81.995677 ◽

2002 ◽

Vol 49 (4) ◽

pp. 551-555 ◽

Cited By ~ 71

Author(s):

Shengyuan Xu ◽

J. Lam ◽

Liqian Zhang

Keyword(s):

Stability Analysis ◽

Singular Systems ◽

State Delay ◽

Discrete Singular Systems

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Robust Preview Control for Uncertain Discrete Singular Systems

Mathematical Problems in Engineering ◽

10.1155/2018/1096793 ◽

2018 ◽

Vol 2018 ◽

pp. 1-9 ◽

Cited By ~ 1

Author(s):

Jiang Wu ◽

Fucheng Liao ◽

Yifan Shao ◽

Shujie Gao ◽

Hao Wang ◽

...

Keyword(s):

Singular Systems ◽

Singular System ◽

Reference Signal ◽

Linear Matrix ◽

Preview Control ◽

Forward Difference ◽

Input Control ◽

Discrete Singular Systems ◽

Error System ◽

The Stability

In this paper, the problem of robust preview control for uncertain discrete singular systems is considered. First of all, by employing the forward difference for uncertain discrete singular systems, the singular augmented error system with the state vector, the input control vector, and the previewable reference signal is derived. Since there is a singular matrix in the system, the existing method cannot be directly applied to this problem. By considering the stability of the transposition system with Linear Matrix Inequality (LMI) method, a new stability criterion for the transposition system is introduced. Then, the robust controller for the augmented error system is obtained, which is regarded as the robust preview controller for the original singular system. At last, the numerical simulation shows the correctness and effectiveness of the results.

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