Stability Analysis of Dynamic General Type-2 Fuzzy Control System With Uncertainty

A growing body of literature has proved that general type-2 fuzzy control systems (GT2 FCSs) are reliable, robust, and safe control systems against severe external disturbances, high levels of noise, and uncertainty that are inevitable in real-world applications. Further studies on the GT2 FCSs are therefore needed to provide new insights into these control systems, in particular over their stability and computational complexity problems. Unlike the existing works on stability analysis of GT2 FCSs in the time domain, the aim of this article is to assess the stability properties of these systems in the frequency domain through a novel intuitive method. Before delving into stability analysis, an initial step involves reducing computational complexity. This is achieved by introducing a streamlined version of the GT2 fuzzy controller (GT2 FC). This simplified architecture is constructed using a series of zSlices-based interval type-2 fuzzy-logic controls (zIT2 FLCs) situated at specific zLevels. Each zIT2 FLC is composed of two embedded type-1 fuzzy FLCs (T1 FLCs). The subsequent phase entails a methodical procedure for assessing stability based on the existence of limit cycles. The initial stage involves the linearization of the simplified GT2 FC through the derivation of its describing function (DF). Next, a combination of the parameter plane approach and the particle swarm optimization (PSO) technique is leveraged. These techniques serve the purpose of pinpointing the regions corresponding to limit cycles and asymptotic stability with a focus on improving the stability boundary. Following this, the analysis shifts toward quantifying the system’s resilience in the face of uncertainty. Stability margins required to generate a limit cycle are calculated using stability equations. This step provides a measure of how robust the closed-loop system remains under varying degrees of uncertainty. Finally, three simulation examples are presented to justify the advantages of the proposed approach.