‎The aim of this paper is to show the importance of analytic hyperbolic geometry introduced in [9]‎. ‎In [1]‎, ‎Ungar and Chen showed that the algebra of the group $SL(2,mathbb C)$ naturally leads to the notion of gyrogroups ‎and gyrovector spaces for dealing with the Lorentz group and its ‎underlying hyperbolic geometry‎. ‎They defined the Chen addition and then Chen model of hyperbolic geomet...

This paper presents a robust ∞ H fuzzy controller for a class of T-S time-delay discrete fuzzy bilinear system (DFBS). Firstly, a discrete robust ∞ H fuzzy controller is proposed to stabilize the T-S time-delay DFBS with disturbance. Secondly, based on the Schur complement and some variable transformation, the stability conditions of the overall fuzzy control system are formulated by linear mat...

This paper is concerned with analyzing a novel model transformation of discrete-time Takagi-Sugeno (T-S) fuzzy systems with time-varying delays and applying it to dynamic output feedback (DOF) controller design. A new auxiliary model is proposed by employing a new approximation for time-varying delay state, and then delay partitioning method is used to analyze the scaled small gain of this auxi...

This paper discusses the stabilization of Takagi–Sugeno (T–S) fuzzy systems with bounded and time-varying input delay. The robust stabilization via state feedback is first addressed, and delay-dependent stabilization conditions are proposed in terms of LMIs. Observer-based feedback stabilization is also discussed for T–S fuzzy input delay systems without uncertainties. A separate design princip...

Robust control theory is an interdisciplinary branch of engineering and applied mathematics literature. Since its introduction in 1980’s, it has grown to become a major scientific domain. For example, it gained a foothold in Economics in the late 1990 and has seen increasing numbers of Economic applications in the past few years. This theory aims to design a controller which guarantees closed-l...

this paper is pertained with the problem of admissibility analysis of uncertain discrete-time nonlinear singular systems by adopting the state-space takagi-sugeno fuzzy model with time-delays and norm-bounded parameter uncertainties. lyapunov krasovskii functionals are constructed to obtain delay-dependent stability condition in terms of linear matrix inequalities, which is dependent on the low...

The paper investigates delay-dependent control and stability analysis for T−S fuzzy systems with a sensor delay. Based on a Lyapunov-Krasovskii function (LKF), a less conservative delay-dependent stability condition in the form of parameterized linear matrix inequalities (PLMIs) is established. In the derivation process, Jensen inequality is introduced to estimate the upper bound of the derivat...

In this paper, a mathematical model based on the T-S fuzzy is proposed to solve fault estimation (FE) and fault-tolerant control (FTC) problem for singular nonlinear time-varying delay (TVD) systems with sensor fault. TVD extremely difficult Laplace transform devised build an equal system free of TVD. Additionally, changed actuator by developed coordinate transformation. A learning estimator fi...

A Takagi-Sugeno (T-S) fuzzy model is used to express non-linear dynamic systems with time-delay in this paper, and an on-line identi® cation algorithm is presented regarding its parameters and structures. A multivariable fuzzy generalized predictive control approach is proposed based on the identi® ed fuzzy model by means of the generalized predictive control principle. The closed-loop stabilit...