H_∞ fault detection and control of Takagi–Sugeno continuous-time conic-type nonlinear systems

Abstract

In this study, control and fault detection are examined for Takagi–Sugeno (T–S) fuzzy continuous-time systems with conic-type nonlinearity. In a conic-type dynamic system, Takagi–Sugeno fuzzy models are applied. A conic-type non-linearity must lie in an n-dimensional hyper-sphere with an uncertain centre to satisfy the restrictive condition. A combined error system of estimation and control error is obtained by combining the observations and the controller. Our main goal is to design an observer and controller for fault detection that minimizes the impact of unknown inputs and faults on the system in terms of the $H_{\mathrm{\infty }}$ performance. The Lyapunov function is used to construct the residual signal using an observer and a controller. Using Linear Matrix Inequalities (LMIs), we can express the performance conditions for $H_{\mathrm{\infty }}$. The scheme's effectiveness is demonstrated with numerical examples.

Keywords:

• T–S fuzzy system
• conic-type nonlinearities
• $H_{\mathrm{\infty }}$ control
• fault detection

AMS Subject Classifications:

• 34H05
• 34H15
• 34H20

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research has been funded by Scientific Research Deanship at University of Ha'il-Saudi Arabia through Project Number RG-23 005.