scholarly journals The Semimartingale Approach to Almost Sure Stability Analysis of a Two-Stage Numerical Method for Stochastic Delay Differential Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Qian Guo ◽  
Xueyin Tao
Keyword(s):  
Differential Equation ◽  
Numerical Experiments ◽  
Time Varying ◽  
Almost Sure Stability ◽  
Stochastic Delay ◽  
Almost Sure Exponential Stability ◽  
Time Varying Delay ◽  
Backward Euler ◽  
Delay Differential ◽  
Varying Delay

Almost sure exponential stability of the split-step backward Euler (SSBE) method applied to an Itô-type stochastic differential equation with time-varying delay is discussed by the techniques based on Doob-Mayer decomposition and semimartingale convergence theorem. Numerical experiments confirm the theoretical analysis.

scholarly journals Observer-Based Robust Control for Switched Stochastic Systems with Time-Varying Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Guoxin Chen ◽  
Zhengrong Xiang ◽  
Hamid Reza Karimi
Keyword(s):  
Robust Control ◽  
Stochastic Systems ◽  
Controller Design ◽  
Average Dwell Time ◽  
Delay Systems ◽  
Time Varying ◽  
Stochastic Delay ◽  
Time Varying Delay ◽  
Switched Stochastic Systems ◽  
Varying Delay

This paper investigates the problem of observer-based robust control for a class of switched stochastic systems with time-varying delay. Based on the average dwell time method, an exponential stability criterion for switched stochastic delay systems is proposed. Then, performance analysis and observer-based robust controller design for the underlying systems are developed. Finally, a numerical example is presented to illustrate the effectiveness of the proposed approach.

scholarly journals Dissipative Delay-Feedback Control for Nonlinear Stochastic Systems with Time-Varying Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Guici Chen ◽  
Jianzhong Zhou ◽  
Yongchuan Zhang
Keyword(s):  
Feedback Control ◽  
Stochastic Systems ◽  
Delay Systems ◽  
Time Varying ◽  
Stochastic Delay ◽  
Time Varying Delay ◽  
Special Cases ◽  
Delay Feedback Control ◽  
Delay Dependent ◽  
Varying Delay

The dissipative delay-feedback control problems for nonlinear stochastic delay systems (NSDSs) based on dissipativity analysis are studied in this paper. Based on the Lyapunov stability theory and stochastic analysis technique, both delay-independent and delay-dependent dissipativity criteria are established as linear matrix inequalities- (LMIs-) based feasibility tests. The obtained results in this paper for the nominal systems include the available results onH∞approach and passivity for stochastic delay systems as special cases. The delay-dependent feedback controller is designed by considering the relationship among the time-varying delay, its lower and upper bound, and its differential without ignoring any terms, which effectively reduces the conservative. A numerical example is given to illustrate the theoretical developments.

scholarly journals Qualitative Analyses of Differential Systems with Time-Varying Delays via Lyapunov–Krasovskiĭ Approach

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1196
Author(s):  
Cemil Tunç ◽  
Osman Tunç ◽  
Yuanheng Wang ◽  
Jen-Chih Yao
Keyword(s):  
Sufficient Conditions ◽  
Zero Solution ◽  
Unperturbed System ◽  
Time Varying ◽  
Time Varying Delay ◽  
Gronwall’S Inequality ◽  
Perturbed System ◽  
Linear Delay ◽  
Delay Differential ◽  
Varying Delay

In this paper, a class of systems of linear and non-linear delay differential equations (DDEs) of first order with time-varying delay is considered. We obtain new sufficient conditions for uniform asymptotic stability of zero solution, integrability of solutions of an unperturbed system and boundedness of solutions of a perturbed system. We construct two appropriate Lyapunov–Krasovskiĭ functionals (LKFs) as the main tools in proofs. The technique of the proofs depends upon the Lyapunov–Krasovskiĭ method. For illustration, two examples are provided in particular cases. An advantage of the new LKFs used here is that they allow to eliminate using Gronwall’s inequality. When we compare our results with recent results in the literature, the established conditions are more general, less restrictive and optimal for applications.

scholarly journals Some New Results on the Lotka-Volterra System with Variable Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Yangzi Hu ◽  
Fuke Wu ◽  
Chengming Huang
Keyword(s):  
Volterra Model ◽  
Time Varying ◽  
Two Dimensional ◽  
Variable Delay ◽  
Volterra System ◽  
Stochastic Delay ◽  
Time Varying Delay ◽  
Varying Delay

This paper discusses the stochastic Lotka-Volterra system with time-varying delay. The nonexplosion, the boundedness, and the polynomial pathwise growth of the solution are determined once and for all by the same criterion. Moreover, this criterion is constructed by the parameters of the system itself, without any uncertain one. A two-dimensional stochastic delay Lotka-Volterra model is taken as an example to illustrate the effectiveness of our result.

scholarly journals Almost Sure andLpConvergence of Split-Step Backward Euler Method for Stochastic Delay Differential Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Qian Guo ◽  
Xueyin Tao
Keyword(s):  
Differential Equation ◽  
Almost Sure Convergence ◽  
Euler Method ◽  
Backward Euler Method ◽  
Variable Delay ◽  
Cantelli Lemma ◽  
Stochastic Delay ◽  
Backward Euler ◽  
Stochastic Delay Differential Equation ◽  
Delay Differential

The convergence of the split-step backward Euler (SSBE) method applied to stochastic differential equation with variable delay is proven inLp-sense. Almost sure convergence is derived from theLpconvergence by Chebyshev’s inequality and the Borel-Cantelli lemma; meanwhile, the convergence rate is obtained.

Stability Analysis of Turning With Periodic Spindle Speed Modulation Via Semidiscretization

2004 ◽  
Vol 10 (12) ◽  
pp. 1835-1855 ◽  
Author(s):  
Tamas Insperger ◽  
Gabor Stepan
Keyword(s):  
Modulation Frequency ◽  
Spindle Speed ◽  
Hopf Bifurcations ◽  
Time Varying ◽  
Single Degree Of Freedom ◽  
Time Varying Delay ◽  
High Modulation ◽  
Speed Modulation ◽  
Delay Differential ◽  
Varying Delay

We investigate a single-degree-of-freedom model of turning with sinusoidal spindle speed modulation and the corresponding delay-differential equation with time-varying delay. The equation is analyzed by the numerical semidiscretization method. Stability charts and chatter frequencies are constructed. Improvement in the efficiency of machining is found for high modulation frequency and for low spindle speed domain. Period-one, period-two (flip), and secondary Hopf bifurcations were detected by eigenvalue analysis.

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