An eigenvalue perturbation result for stability bound with respect to biased structured perturbations

AbstractUsing a novel approach, we present some new explicit criteria for global exponential stability of the zero solution of general nonlinear time-varying Volterra difference equations. Furthermore, an explicit stability bound for equations subject to nonlinear time-varying perturbations is given. Finally, the obtained results are used to study uniform attraction of equilibrium of discrete-time bidirectional associative memory (BAM) neural networks. Some illustrative examples are given.

Download Full-text

Stability of circular Couette flow with variable inner cylinder speed

Journal of Fluid Mechanics ◽

10.1017/s0022112082002948 ◽

1982 ◽

Vol 123 ◽

pp. 43-57 ◽

Cited By ~ 13

Author(s):

G. P. Neitzel

Keyword(s):

Angular Velocity ◽

Incompressible Fluid ◽

Viscous Incompressible Fluid ◽

Outer Cylinder ◽

Finite Amplitude ◽

Reverse Direction ◽

Stability Bound ◽

Concentric Cylinders ◽

Theory Result ◽

Stability Enhancement

Energy & ability theory is employed to study the finite-amplitude stability of a viscous incompressible fluid occupying the space between a pair of concentric cylinders when the inner-cylinder angular velocity varies linearly with time. For the case with a fixed outer cylinder and increasing inner-cylinder speed, we find an enhancement of stability, consistent with a linear-theory result due to Eagles. When the inner-cylinder speed decreases, we find an initially decreased stability bound, indicating the possibility of hysteresis, while, if the inner cylinder is allowed to reverse direction and linearly increase in speed, we find significant stability enhancement.

Download Full-text

Fuzzy Controllers for Nonaffine-in-Control Singularly Perturbed Switched Systems

Mathematical Problems in Engineering ◽

10.1155/2015/896413 ◽

2015 ◽

Vol 2015 ◽

pp. 1-11 ◽

Cited By ~ 2

Author(s):

Linna Zhou ◽

Qianjin Wang ◽

Xiaoping Ma ◽

Chunyu Yang

Keyword(s):

Switched Systems ◽

Fuzzy Controller ◽

Controller Design ◽

Design Method ◽

Singularly Perturbed ◽

Dynamic State ◽

Linear Matrix ◽

Closed Loop System ◽

Stability Bound ◽

Takagi Sugeno

This paper investigates the problem of fuzzy controller design for nonaffine-in-control singularly perturbed switched systems (NCSPSSs). First, the NCSPSS is approximated by Takagi-Sugeno (T-S) models which include not only state but also control variables in the premise part of the rules. Then, a dynamic state feedback controller design method is proposed in terms of linear matrix inequalities. Under the controller, stability bound estimation problem of the closed-loop system is solved. Finally, an example is given to show the feasibility and effectiveness of the obtained methods.

Download Full-text

Frames for operators in Banach spaces via semi-inner products

International Journal of Wavelets Multiresolution and Information Processing ◽

10.1142/s0219691316500119 ◽

2016 ◽

Vol 14 (03) ◽

pp. 1650011 ◽

Cited By ~ 1

Author(s):

Bahram Dastourian ◽

Mohammad Janfada

Keyword(s):

Banach Space ◽

Banach Spaces ◽

Reproducing Kernel ◽

Atomic System ◽

Inner Product ◽

Reconstruction Formula ◽

Frame Operator ◽

Atomic Systems ◽

Perturbation Result ◽

Reproducing Kernel Banach Spaces

In this paper, the concept of a family of local atoms in a Banach space is introduced by using a semi-inner product (s.i.p.). Then this concept is generalized to an atomic system for operators in Banach spaces. We also give some characterizations of atomic systems leading to new frames for operators. In addition, a reconstruction formula is obtained. The characterizations of atomic systems allow us to state some results for sampling theory in s.i.p reproducing kernel Banach spaces. Finally, we define the concept of frame operator for these kinds of frames in Banach spaces and then we establish a perturbation result in this framework.

Download Full-text