Technical science and innovation


. The pulse-frequency control systems are widely used in radar, space industry, for control of technological processes and robots and many other areas. Today, there are various approximate and accurate methods for the analysis and synthesis of pulse-frequency systems (PFS). However, the area of the practical application of the existed methods is mainly limited to single-variable systems. The classical methods provide the consideration of the initial structures of pulse-frequency systems as a whole. This article proposes the decomposition method for modeling and research pulse-frequency automatic control systems. The method is based on the mathematical apparatus of signal-flow graphs. We can use the method for analysis and synthesis of both single-variable and multivariable automatic control systems with pulse-frequency modulation

First Page


Last Page





1. Tsyipkin Ya.Z., Popkov Yu.S., Theory of nonlinear impulse systems, M., Nauka, 1973.

2. Kuntsevich V.M. Chehovoy Yu.N. Nonlinear control systems with frequency and pulse-width modulation, Kiev, Tekhnika, 1970.

3. Zavalishchin S.T. and Sesekin A.N.. Dynamic Impulse Systems. Theory and Applications. Mathematics and its Applications. Kluwer Academic Publishers Group, Dordrecht, 1997.

4. Yang T., Impulsive control. IEEE Transactions on Automatic Control, 44, 1081-1083, 1999.

5. Rogers E., Galkowski K., and Owens D.. Control Systems Theory and Applications for Linear Repetitive Processes, volume 349 of Lecture Notes in Control and Information Sciences. Springer-Verlag, Berlin, 2007.

6. Chellaboina V., Bhat S.P., Haddad W.M., An invariance principle for nonlinear hybrid and impulsive dynamical systems, American Control Conference 2000. Proceedings of the 2000, vol. 5, pp. 3116-3122, 2000.

7. Hou Ling, Michel Anthony N., Unifying theory for stability of continuous, discontinuous, and discrete-time dynamical systems. Nonlinear Analysis: Hybrid Systems, vol. 1, no. 2, pp. 154-172, 2007.

8. Goebel R., Sanfelice Ricardo G., and Teel Andrew R., Hybrid Dynamical Systems. Princeton University Press, 227p., 2012.

9. Manson G., Worden K., Reed P., Analysis of Nonlinear System Response to an Impulse Excitation. Nonlinear Dynamics, vol. 2, pp.297-308, 2014. doi: 10.1007/978-3-319-04522-1_28.

10. Ríos H., Hetel L., and Efimov D.. Nonlinear Impulsive Systems: 2D Stability Analysis Approach. Automatica, Elsevier, 2017. ffhal-01437308f

11. Briat C. and Seuret A.. Convex dwell-time characterizations for uncertain linear impulsive systems. IEEE Transactions on Automatic Control, 57(12):3241–3246, 2012.

12. Kaganov V.I., Tereschenko S.V., Computer analysis of an impulse automatic control system. Vestnik Voronejskogo instituta MVD Rossii. 2011. №2. S.6-13.

13. Shishlakov V.F., Synthesis of nonlinear pulse control systems in the time domain. Izvestiya vuzov. Ser. Priborostroenie. 2003. №12. S.25-30.

14. Sira-Ramirez H., Llanes-Santiago O., Adaptive PWM Regulation Schemes in Switched Controlled Systems, Proc. of the IFAC World Congress, Sydney Australia, volume 10, 57-60, 1993.

15. Kadirov A., Decomposition bases of modeling and research of control systems based on dynamic graphs. Tashkent, Iqtisod-Moliya, 224 s., 2015.

16. Kadirov A., Kadirova A., Modeling and research of nonlinear amplitude-pulse systems based on dynamic graphs. Tashkent, Navruz, 236 s., 2018.

17. Kadirova A., Kadirova D., and Bakhracheva J., Compensation of delay in multivariable control systems using the method of dynamic graphs. Journal of Technical University of Gabrovo, volume 58, 2019, p.47-52. http://izvestia.tugab.bg/index.php?m=20and tom=16.



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.