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 | 20180813141028.0 | ||
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 |
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