Liapunov Stability Criteria for Continuous Systems Under Parametric Excitation

1972 ◽  
Vol 39 (1) ◽  
pp. 244-250 ◽  
Author(s):  
T. H. Lee ◽  
C. S. Hsu
Keyword(s):  
Parametric Excitation ◽  
Direct Method ◽  
Continuous Systems ◽  
Panel Flutter ◽  
Stability Criteria ◽  
Use Of Time ◽  
Liapunov Direct Method ◽  
Liapunov Functionals ◽  
Adjoint Operators ◽  
Extremal Properties

A Liapunov direct method is developed here to derive stability criteria for continuous systems under parametric excitation. The method makes use of time-dependent Liapunov functionals and the extremal properties of Rayleigh quotients of self-adjoint operators. The application of the method entails solving an eigenvalue problem with the variable t appearing in the problem strictly as a parameter. As examples of application the method is applied to (a) a clamped column under the action of periodic axial load, and (b) the panel flutter problem with the panel also subjected to periodic in-plane load. The calculated results for the first example show improvement over those obtained previously.

Thermally Induced Instability of Laminated Beams and Plates

1996 ◽  
Vol 63 (4) ◽  
pp. 884-890 ◽  
Author(s):  
A. Tylikowski ◽  
R. B. Hetnarski
Keyword(s):  
Stochastic Stability ◽  
Direct Method ◽  
Wide Band ◽  
Temperature Fields ◽  
Time And Space ◽  
Thermally Induced ◽  
Stability Problems ◽  
Linear Elastic ◽  
Liapunov Direct Method ◽  
Short Time

A theoretical investigation of dynamic stability for linear elastic structures due to non-uniform, time and space-dependent stochastic temperature fields is presented. The study is based on the reformulation of stochastic stability problems as a stability of Itoˆ type equations in some appropriate Hilbert space and is adopted for stability problems of structures with time and space-dependent stochastic coefficients. Uniform stochastic stability criteria of the structure equilibrium are derived using the Liapunov direct method. The energy-like functional and the generalized ltoˆ lemma are used to derive the sufficient stability conditions of the equilibrium state. A symmetrically laminated crossply plate subjected to the wide-band Gaussian temperature distribution and a laminated beam subjected to local short-time heatings are analysed in detail.

Asymptotic stability criteria for delay-differential equations

1988 ◽  
Vol 110 (1-2) ◽  
pp. 31-44
Author(s):  
L.C. Becker ◽  
T.A. Burton
Keyword(s):  
Differential Equations ◽  
Direct Method ◽  
Infinite Delay ◽  
Functional Differential Equations ◽  
State Variables ◽  
Stability Criteria ◽  
Bounded State ◽  
Functional Differential ◽  
Delay Differential ◽  
Liapunov's Direct Method

SynopsisThis paper is concerned with the problem of showing uniform stability and equiasymptotic stability of thezero solution of functional differential equations with either finite or infinite delay. The investigations are based on Liapunov's direct method and attention is focused on those equations whose right-hand sides are unbounded for bounded state variables.

Impulsive state feedback control during the sulphitation reaction in process of manufacture of sugar

2020 ◽  
pp. 2050076
Author(s):  
Guoping Pang ◽  
Xianbo Sun ◽  
Zhiqing Liang ◽  
Silian He ◽  
Xiaping Zeng
Keyword(s):  
Periodic Solution ◽  
Feedback Control ◽  
Limit Cycles ◽  
Switched Systems ◽  
State Feedback ◽  
State Feedback Control ◽  
Continuous Systems ◽  
Stability Criteria ◽  
Impulsive State Feedback Control ◽  
Existence And Stability

In this paper, the system with impulsive state feedback control corresponding to the sulphitation reaction in process of manufacture of sugar is considered. By means of square approximation and a series of switched systems, the periodic solution is approximated by a series of continuous hybrid limit cycles. Similar to the analysis of limit cycles of continuous systems, the existence and stability criteria of the order-1 periodic solution are obtained. Further, numerical analysis and discussion are given.

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