Stability of pulse-modulated systems with a monotone equivalent nonlinearity in the modulator. (English. Russian original) Zbl 1143.93324
Vestn. St. Petersbg. Univ., Math. 40, No. 4, 294-301 (2007); translation from Vestn. St-Peterbg. Univ., Ser. I, Mat. Mekh. Astron. 2007, No. 4, 91-99 (2007).
Summary: A pulse-modulated system described by a functional differential equation is considered. Sufficient frequency conditions for global stability are obtained by using the averaging method and a frequency theorem.
MSC:
| 93C23 | Control/observation systems governed by functional-differential equations |
| 93D09 | Robust stability |
| 93C10 | Nonlinear systems in control theory |
| 93C80 | Frequency-response methods in control theory |
References:
| [1] | N. E. Barabanov, Sib. Mat. Zh. 28(2), 21–34 (1987). · Zbl 0656.34050 · doi:10.1007/BF00970863 |
| [2] | N. V. Kuznetsov, Differ. Uravn. Protsessy Uprvalen. (electronic), No. 3 (2004), http://www.neva.ru/journal . |
| [3] | A. Kh. Gelig, I. E. Zuber, and A. N. Churilov, Stability and Stabilization of Nonlinear Systems (Izd. S.-Peterburg. Univ., St. Petersburg, 2006) [in Russian]. |
| [4] | A. Kh. Gelig and A. N. Churilov, Stability and Oscillations of Nonlinear Pulse-Modulated Systems (Birkhäuser, Boston, 1998). · Zbl 0935.93001 |
| [5] | V. A. Yakubovich, G. A. Leonov, and A. Kh. Gelig, Stability of Stationary Sets in Control Systems with Discontinuous Nonlinearities (World Sci., New Jersey, 2004). · Zbl 1054.93002 |
| [6] | A. Kh. Gelig, Prikl. Mat. Mekh. 62(8), 231–238 (2003). |
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