Non-PDC-based local stabilization conditions of discrete-time nonhomogeneous fuzzy Markov jump systems with dynamic event-triggered mechanism

Abstract

Centered on the non-parallel distribution compensation (non-PDC) control scheme, this paper attempts to tackle the issue of event-triggered local stabilization for nonhomogeneous Takagi–Sugeno (T-S) fuzzy Markov jump systems (FMJSs) that take mismatched fuzzy basis functions (FBFs) into consideration. With this aim, this paper presents a framework for formulating local stabilization criteria built on fuzzy Lyapunov functions, establishing criteria for defining an attraction region within an invariant ellipsoidal set and incorporating the occurrence of energy-constrained disturbances into the local control problem. In addition, the mismatch problem encountered in designing an event-triggered fuzzy controller is resolved by integrating a congruent transformation matrix that relies on mismatched fuzzy basis functions while preserving the dependence of the Lyapunov function on the original premise functions. Furthermore, to simultaneously cope with complex and diverse system parameter constraints, a systematic and less conservative method is proposed, which involves centralizing nonhomogeneous transition probabilities (TPs), transforming mismatched fuzzy basis functions into fuzzy basis function errors, and employing relaxation techniques.