Number Of Stability Conditions Research Articles

H ∞ fault detection for 2-D T–S discrete stochastic fuzzy systems

ABSTRACT This paper is concerned with fault detection (FD) problem for a class of two-dimensional (2-D) Takagi–Sugeno (T–S) discrete stochastic fuzzy systems. Based on the parallel distributed compensation (PDC), the fuzzy FD filter and the dynamics of FD system are constructed. Since the multiplicative property of the FD system would drastically increase the number of the stability conditions, a method of decoupling based on dimension expansion is used. By decoupling, the number of LMI-based stability conditions is reduced to r from by the conventional method. Then, the fuzzy FD filter is designed. The corresponding fuzzy FD system is proved to be mean-square asymptotically stable and satisfies the attenuation level for all disturbances. In addition, a theorem is proposed to prove that the stability conditions based on decoupling method are equivalent to those of conventional method. Finally, simulation examples are provided to demonstrate the usefulness of the proposed design methods.

Computational Effective Stability Conditions for Time-delay Fuzzy Systems

This paper investigates the system stability of the time-delay fuzzy-model-based control systems based on delay-independent and -dependent approaches. LMI-based delay-independent and -dependent stability conditions are derived to guarantee the system stability using Lyapunov-based technique. It can be seen that some existing stability analysis approaches require high computational demand to solve the solution due to the large number of stability conditions. Consequently, feasible solution may not be obtained with the use of numerical methods due to the limitation of the computer system especially for complicated fuzzy systems with a large number of rules. In this paper, under a particular system formulation, the number of stability conditions can be reduced to alleviate the computational demand on searching for the solution. Furthermore, the stability conditions offer a larger upper bound of time delay compared with some existing approaches. LMI-based performance conditions are also derived to guarantee the system performance. Simulation examples are given to illustrate the merits of the proposed approaches.