TY - JOUR UR - http://lib.ugent.be/catalog/pug01:160996 ID - pug01:160996 LA - eng TI - Exponential stability of slowly time-varying nonlinear systems PY - 2002 JO - (2002) MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS SN - 0932-4194 PB - 2002 AU - Peuteman, Joan AU - Aeyels, Dirk TW06 801000317632 0000-0002-3031-7215 AB - Let (x) over dot = f (x, t, t/alpha) be a time-varying vector field depending on t containing a regular and a slow time scale (alpha large). Assume there exist a k(tau) greater than or equal to 1 and a gamma(tau) such that parallel tox(tau)(t, t(0), x(0))parallel to less than or equal to k(tau)e(-gamma(tau)(t-t0))parallel tox(0)parallel to, with x(tau)(t, t(0), x(0)) the solution of the parametrized system (x) over dot = f (x, t, tau) with initial state x(0) at t(0) We show that for a sufficiently large (x) over dot = f (x, t, t/alpha) is exponentially stable when "on average" gamma(tau) is positive. The use of this result is illustrated by means of two examples. First, we extend the circle criterion. Second, exponential stability for a pendulum with a nonlinear slowly time-varying friction attaining positive and negative values is discussed. ER -Download RIS file
00000nam^a2200301^i^4500 | |||
001 | 160996 | ||
005 | 20161219153857.0 | ||
008 | 040114s2002------------------------eng-- | ||
022 | a 0932-4194 | ||
024 | a 000178262300002 2 wos | ||
024 | a 1854/LU-160996 2 handle | ||
024 | a 10.1007/s004980200008 2 doi | ||
040 | a UGent | ||
245 | a Exponential stability of slowly time-varying nonlinear systems | ||
260 | c 2002 | ||
520 | a Let (x) over dot = f (x, t, t/alpha) be a time-varying vector field depending on t containing a regular and a slow time scale (alpha large). Assume there exist a k(tau) greater than or equal to 1 and a gamma(tau) such that parallel tox(tau)(t, t(0), x(0))parallel to less than or equal to k(tau)e(-gamma(tau)(t-t0))parallel tox(0)parallel to, with x(tau)(t, t(0), x(0)) the solution of the parametrized system (x) over dot = f (x, t, tau) with initial state x(0) at t(0) We show that for a sufficiently large (x) over dot = f (x, t, t/alpha) is exponentially stable when "on average" gamma(tau) is positive. The use of this result is illustrated by means of two examples. First, we extend the circle criterion. Second, exponential stability for a pendulum with a nonlinear slowly time-varying friction attaining positive and negative values is discussed. | ||
598 | a A1 | ||
100 | a Peuteman, Joan 0 801000953384 | ||
700 | a Aeyels, Dirk u TW06 0 801000317632 0 0000-0002-3031-7215 | ||
650 | a Technology and Engineering | ||
653 | a exponential stability | ||
653 | a differential equations | ||
653 | a Liapunov stability | ||
653 | a slowly time-varying systems | ||
653 | a Lur'e systems | ||
653 | a pendulum | ||
653 | a DIFFERENTIAL-EQUATIONS | ||
653 | a ASYMPTOTIC STABILITY | ||
773 | t MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS g Math. Control Signal Syst. 2002. 15 (3) p.202-228 q 15:3<202 | ||
856 | 3 Full Text u https://biblio.ugent.be/publication/160996/file/716436 z [ugent] y Peuteman_2002_MCSS_15_3_202.pdf | ||
920 | a article | ||
852 | x EA b TW08 | ||
922 | a UGENT-EA |
All data below are available with an Open Data Commons Open Database License. You are free to copy, distribute and use the database; to produce works from the database; to modify, transform and build upon the database. As long as you attribute the data sets to the source, publish your adapted database with ODbL license, and keep the dataset open (don't use technical measures such as DRM to restrict access to the database).
The datasets are also available as weekly exports.