H

This paper investigates the problem of H∞ filtering for class discrete-time Lipschitz nonlinear singular systems with measurement quantization. Assume that the system measurement output is quantized by a static, memoryless, and logarithmic quantizer before it is transmitted to the filter, while the quantizer errors can be treated as sector-bound uncertainties. The attention of this paper is focused on the design of a nonlinear quantized H∞ filter to mitigate quantization effects and ensure that the filtering error system is admissible (asymptotically stable, regular, and causal), while having a unique solution with a prescribed H∞ noise attenuation level. By introducing some slack variables and using the Lyapunov stability theory, some sufficient conditions for the existence of the nonlinear quantized H∞ filter are expressed in terms of linear matrix inequalities (LMIs). Finally, a numerical example is presented to demonstrate the effectiveness of the proposed quantized filter design method

Fuzzy Laplace Transforms for Derivatives of Higher Orders

In this paper, we find the formula of fuzzy derivative of the third order and fourth order  and  find the fuzzy Laplace transforms for the fuzzy derivative of the above mentioned orders by using generalized H-differentiability. Keywords: Fuzzy numbers, generalized H-differentiability, Fuzzy Laplace transform

An LP V/H∞ integrated Vehicle Dynamic Controller

International audienceThis paper is concerned with the design and analysis of a new multivariable LP V /H∞ (Linear Parameter Varying) robust control design strategy for Global Chassis Control. The main objective of this study is to handle critical driving situations by activating several controller subsystems in a hierarchical way. The proposed solution consists indeed in a two-step control strategy that uses semi-active suspensions, active steering and electro-mechanical braking actuators. The main idea of the strategy is to schedule the 3 control actions (braking, steering and suspension) according to the driving situation evaluated by a specific monitor. Indeed, on one hand, rear braking and front steering are used to enhance the vehicle yaw stability and lateral dynamics, and on the other hand, the semi-active suspensions to improve comfort and car handling performances. Thanks to the LP V /H∞ framework, this new approach allows to reach a smooth coordination between the various actuators, to ensure robustness and stability of the proposed solution, and to significantly improve the vehicle dynamical behavior. Simulations have been performed on a complex full vehicle model which has been validated using data obtained from experimental tests on a real Renault Mégane Coupé. Moreover, the suspension system uses Magneto-Rheological dampers whose characteristics have been obtained through experimental identification tests. A comparison between the proposed LPV/H∞ control strategy and a classical LTI/H∞ controller is performed using the same simulation scenarios and confirms the effectiveness of this approach

Global existence of solutions for fuzzy second-order differential equations under generalized H-differentiability

AbstractIn this paper, we study the global existence of solutions for second-order fuzzy differential equations with initial conditions under generalized H-differentiability. Second derivative of the H-difference of two functions under generalized H-differentiability is obtained. Two theorems which assure global existence of solutions for second-order fuzzy differential equations are given and proved. Some examples are given to illustrate these results

Non-commutative World-volume Geometries: Branes on SU(2) and Fuzzy Spheres

The geometry of D-branes can be probed by open string scattering. If the background carries a non-vanishing B-field, the world-volume becomes non-commutative. Here we explore the quantization of world-volume geometries in a curved background with non-zero Neveu-Schwarz 3-form field strength H = dB. Using exact and generally applicable methods from boundary conformal field theory, we study the example of open strings in the SU(2) Wess-Zumino-Witten model, and establish a relation with fuzzy spheres or certain (non-associative) deformations thereof. These findings could be of direct relevance for D-branes in the presence of Neveu-Schwarz 5-branes; more importantly, they provide insight into a completely new class of world-volume geometries.Comment: 19 pages, LaTeX, 1 figure; some explanations improved, references adde