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# On growth conditions for uniform asymptotic stability of damped linear oscillators with time-varying coefficients

2017-11-20

Title: On growth conditions for uniform asymptotic stability of damped linear oscillators with time-varying coefficients

Reporter: Professor Jitsuro Sugie（Shimane University, Japan）

Time: November 21,2017(Tuesday) PM 4:00-5:00

Location: A1101# room, Innovation Park Building

Contact: Prof. LU Yufeng(tel:84708352)

Abstract: This talk clarifies the relationship between some sufficient conditions which guaranteethat the equilibrium of the damped harmonic oscillator $$x’’ +h(t)x’+\omega^2 x=0$$ is uniformly asymptotically stable, where $h:[0,\infty)\to [0,\infty)$ is locally integrable.Those conditions work to suppress the rapid growth of the frictional force expressedby the integral amount of the damping coefficient $h$. The obtained sufficient conditions are compared with known conditions for uniform asymptotic stability. A relationship diagram is shown to facilitate understanding of the  conditions. By giving a concrete example, remaining problems are pointed out.

The brief introduction to the reporter: Jitsuro Sugie, a professor of Shimane University, Japan. He achieved his Ph.D in Mathematics from Northeastern University in March, 1990. His main research areas are ODEs, dynamical systems, differential equations, bio-mathematics and so on.