Finite-time stability of solutions for non-instantaneous impulsive systems and application to neural networks

Stability analysis of T-S fuzzy state-dependent impulsive nonlinear systems via an extended functional-based approach

“…Then one gets condition (15). By differentiating equation (18) with respect to t along the state trajectory of system (5), one can obtain the following equation:…”

“…In recent decades, fuzzy logic [14] has gained significant prominence among researchers from diverse academic disciplines, owing to its capacity to offer robust solutions for a wide array of challenges characterized by uncertainty and nonlinear control problems [14][15][16][17]. Among the various methodologies for fuzzy logic control, the Takagi-Sugeno (T-S) fuzzy model introduced in [18] has attained substantial recognition as a potent instrument for the investigation of fuzzy control systems.…”

“…Consequently, this model enables the stabilization of nonlinear dynamical sys-tems through establishing a comprehensive linear system theory [14,18]. An abundance of scholars has dedicated their efforts to the investigation and exploration of the stability and stabilization aspects pertaining to T-S fuzzy impulsive systems over the course of recent years [6,[15][16][17]19]. For instance, the authors have successfully realized exponential stabilization of T-S fuzzy stochastic dynamic networks by capitalizing on the utilization of state-dependent impulsive controllers, as explicated in [16].…”

Finite‐time mixed ℋ∞$$ {\mathscr{H}}_{\infty } $$ and passive filtering for nonlinear singular systems under fading channels

“…Finite-time stability was defined as if the state of a system not exceeding a specified bound of the initially bounded state. 13 Therefore, finite-time stabilization has been more meaningful than Lyapunov stabilization in practical applications, and researchers have achieved remarkable results. 9,14 In particular, the literature 15 addressed the quantized finite-time non-fragile mixed  ∞ and passivity filter design problem for singular Markovian Jump systems.…”

“…For instance, temperature regulation, pressure management, robot control systems, brake systems, and aircraft control systems all require the control process to be completed within a limited time. Finite‐time stability was defined as if the state of a system not exceeding a specified bound of the initially bounded state 13 . Therefore, finite‐time stabilization has been more meaningful than Lyapunov stabilization in practical applications, and researchers have achieved remarkable results 9,14 .…”