A Stability Criterion for Arbitrarily Switched Second Order LTI Systems

2007 ◽  
Author(s):  
Z. H. Huang ◽  
C. Xiang ◽  
H. Lin ◽  
T. H. Lee
Keyword(s):  
Stability Criterion ◽  
Second Order

Dynamic Stability of Wave-Convection Transport

1982 ◽  
Vol 24 (4) ◽  
pp. 225-227
Author(s):  
M. D. Greenberg ◽  
C. Y. Harrell
Keyword(s):  
Dynamic Stability ◽  
Nonlinear Equations ◽  
Parameter Space ◽  
Stability Criterion ◽  
Practical Interest ◽  
Single Equation ◽  
Sine Wave ◽  
Second Order ◽  
Spherical Object

A flexible inextensible horizontal belt is assumed to be formed, by closely spaced vertical push rods, into a traveling sine wave. A spherical object resting at the bottom of a trough will tend to be convected with the trough as the wave travels. The dynamic stability of such wave-convection transport is considered. Assuming the wave to be shallow, the governing nonlinear equations are expanded (through second order) in the ‘shallowness parameter’, and thus reduced to a single equation, essentially of forced Duffing type, which is integrated numerically, over the parameter space of practical interest, to yield a stability criterion.

scholarly journals Stability of Second-Order Asymmetric Linear Mechanical Systems With Application to Robot Grasping

2005 ◽  
Vol 72 (6) ◽  
pp. 966-968 ◽  
Author(s):  
Amir Shapiro
Keyword(s):  
Linear System ◽  
Upper Bound ◽  
Stability Criterion ◽  
Mechanical Systems ◽  
Second Order ◽  
Symmetric System ◽  
Analytical Criterion ◽  
Physical Effects ◽  
Robot Grasping ◽  
The Stability

This technical correspondence presents a surprisingly simple analytical criterion for the stability of general second-order asymmetric linear systems. The criterion is based on the fact that if a symmetric system is stable, adding a small amount of asymmetry would not cause instability. We compute analytically an upper bound on the allowed asymmetry such that the overall linear system is stable. This stability criterion is then applied to robot grasping arrangements which, due to physical effects at the contacts, are asymmetric mechanical systems. We present an application of the stability criterion to a 2D grasp arrangement.

scholarly journals A one-step method for the numerical solution of ordinary non-linear second-order differential equations based upon lobatto four-point quadrature formula

1973 ◽  
Vol 15 (2) ◽  
pp. 193-201 ◽  
Author(s):  
K. D. Sharma ◽  
R. G. Gupta
Keyword(s):  
Differential Equation ◽  
Stability Criterion ◽  
Truncation Error ◽  
Order Differential Equation ◽  
Second Order ◽  
Local Truncation Error ◽  
Step Method ◽  
Second Order Differential Equations ◽  
Computational Comparisons ◽  
One Step

AbstractThis paper describes a one-step method besed upon the Lobatto four-point quadreture formula for the numerical integration of differential: y″(x) = f(x, y(x), y'(x)); y(x0)=y0, y'(x0)=y'0. The method has a local truncation error 0(h6) in y(x) and 0(h5) in y′(x). In the case of linear second-order differential equation, a stability criterion has been developed. Theoretical and computational comparisons of the new method existing method is discussed.

scholarly journals Uniformly asymptotic stability of second-order linear time-varying systems

2020 ◽  
Vol 12 (9) ◽  
pp. 168781402095509
Author(s):  
Da-Ke Gu ◽  
Chao Lu
Keyword(s):  
Asymptotic Stability ◽  
Stability Criterion ◽  
Linear Time ◽  
Second Order ◽  
State Feedback Control ◽  
Time Varying ◽  
Order Linear ◽  
Time Varying Systems ◽  
Uniformly Asymptotic Stability ◽  
The Stability

This paper is concerned with the stability of second-order linear time-varying systems. By utilizing the Lyapunov approach, a generally uniformly asymptotic stability criterion is obtained by adding the system matrices into the quadratic Lyapunov candidate function. In the case of the derivative of the Lyapunov candidate function is semi-positive definite, the stability criterion is also efficient. Based on the proposed results, the systems with uncertain disturbances such as structured independent and structured dependent perturbations are considered. Using the matrix measure and the singular value theory, the bounds of the uncertainties are obtained that guarantee the system uniformly asymptotically stable, while the bounds of state feedback control input are also derived to stabilize the second-order linear time-varying systems. Finally, several numerical examples are given to prove the validity and correctness of the proposed criteria with existing ones.

scholarly journals Theory of Frequency Captured of Eccentric Rotor by Vibration Environment with Same Direction

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Su Ming ◽  
Li Rong ◽  
Xie Zhiping ◽  
Zheng Jiming
Keyword(s):  
Differential Equation ◽  
Stability Criterion ◽  
Periodic Coefficient ◽  
Second Order ◽  
Frequency Synchronization ◽  
Synchronization Problem ◽  
Eccentric Rotor ◽  
Small Parameters ◽  
The Stability ◽  
Rotating Bodies

Aiming at the frequency synchronization phenomena of oscillating or rotating bodies, this paper proposes a novel solution to address the self-synchronization problem of vibration systems. An integral mean method with small parameters and periodic coefficient (IMM-SPPC) is proposed, which converts the relative motion of the electrically driven eccentric rotor and the vibration environment into a second-order periodic coefficient differential equation. Through the calculation of the equilibrium point of the second-order periodic coefficient differential equation and the study of its stability, the synchronization criterion and the stability criterion of the eccentric rotor and the vibration environment are deduced. The simulation results show the validity of the deduced synchronization criterion and stability criterion. The proposed IMM-SPPC provides a new way for studying vibration synchronization.

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