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"Humanities and Science University Journal" №8, 2014

Using Сomputer Modeling to Study Impulsive Systems with Uncertainties and Monotonic Non-Linear Characteristics

N. A. Tseligorov, E. N. Tseligorova, G. М. Mafura
Price: 50 руб.
 This paper focuses on the use of computer modeling to study the uncertainty on the
absolute robust stability of nonlinear impulsive control systems (NICS). We have
considered a multivariate mathematical model of NICS. The criterion for an absolute
stability of the equilibrium of an impulsive system with a monotonous nonlinear characteristic is converted to a polynomial expression, which is more suitable for future
analysis. We have proposed a further investigation of the expression to conduct a modifi ed root locus method. The study of robust stability of NICS is carried out by going to the interval coeffi cients of the transfer function based on strong Kharitonov’s theorem and the use of a modifi ed root locus method for interval polynomials.

nonlinear impulsive control systems, absolute stability, uncertainty, robust stability, interval polynomial, root locus, criterion of absolute stability

1. Tseligorov, N.A., Mafura, G.M. The reasons for the occurrences of interval
parameters in mathematical models during the investigation of robust stability of control systems. Inzhenernyj vestnik Dona, 2012, 4. Retrieved from http://ivdon.ru/magazine/archive/n4p1y2012/1277
2. Tseligorov, N.A., Mafura, G.M. Using the modeling complex “Stability” for
investigating nonlinear impulse control systems with uncertainties. In Computer
Modeling 2013: Proceedings of the international scienti fi c and technical conference.
2013, St. Petersburg: publisher Polytechnic University. Pp. 163–168.
3. Serkov, V.I., Tseligorov, N.A. Analysis of absolute stability of multidimensional
NICS through algebraic modi fi cation of criteria, gotten through bilinear transformation.
Publisher RAN Technical Cybernetics, 1993, 4, 21–28.
4. Tsipkin, Ya.Z., Popkov, Yu.S. Theory of nonlinear impulsive systems. 1973,
Moscow: Nauka.
5. Tseligorov, N.A., Tseligorova, E.N. Using a modified root locus method
to investigate the robust absolute stability of a multidimensional control system.
Identi fi cation systems and control problems. In Proceedings of the Sixth international
conference SICPRO ‘07. 29 Jan – 1 Feb 2007. ICS RAS, No. 13034.
6. Tseligorov, N.A., Tseligorova, E.N. The algebraic aspect of the investigation of
robust and absolute stability of multidimensional control systems. In Materials of the
fourth scienti fi c conference “System synthesis and applied synergetic”. 2011, Taganrog: publisher TTI SFY. Pp. 348–356.
7. Kharitonov, V.L. Stability of nested families of polynomials. 1995, No. 11.
Pp. 169–182.
Price: 50 рублей
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