RESEARCH OF STABILIZATION CONDITIONS AND ROBUST STABILITY OF DISCRETE ALMOST CONSERVATIVE SYSTEMS

Olena Teteriatnyk

Abstract


Conditions for the stabilizability of discrete almost conservative systems in which the coefficient matrix of a conservative part has no multiple eigenvalues are investigated.

It is known that a controllable system will be stabilized if its coefficient matrix is asymptotically stable.

The system stabilization algorithm is constructed on the basis of the solvability condition for the Lyapunov equation and the positive definiteness of P0 and Q1.

This theorem shows how to find the parameters of a controlled system under which it will be asymptotically stable for sufficiently small values of the parameter e (P > 0, Q > 0).

In addition, for a small parameter e  that determines the almost conservatism of the system, an interval is found in which the conditions for its stabilizability are satisfied (Theorem 2).

Keywords


robust stability; almost conservative systems; Lyapunov equation

Full Text:

PDF

References


Koshlyakov, V. N. (1972). Teorija giroskopicheskih kompasov. Moscow: Nauka, 344.

Novytskyy, V. V., Zinchuk, M. O., Teteriatnyk, O. V. (2016). Stabilization and robust stability of continuous almost conservative systems. Vìsnik Zaporìzʹkogo nacìonalʹnogo unìversitetu. Fìziko-matematičnì nauki, 1, 184–191.

Zinchuk, M. O., Novytskyy, V. V. (2007). Stability and stabilization linear parametric dynamic systems. Zbirnyk prats Instytutu matematyky Natsionalnoi akademii nauk Ukrainy, 4 (2), 58–71.

Barnett, S., Cameron, R.G. (1985). Introduction to Mathematical Control Theory. Oxford: Clarendon press, 404.

Zinchuk, M. O., Svyatovets, I. F., Teteriatnyk, O. V. (2016). On asymptotic solutions of matrix equations Lyapunov and Riccati for almost conservative systems. Visnyk Zaporizkoho natsionalnoho unyversytetu: Zbirnyk naukovykh prats. Fizyko-matematychni nauky, 2, 110–121.

Novytskyy, V. V., (2004). Rivniannia Liapunova dlia maizhe konservatyvnykh system. NAN Ukrainy. Instytut matematyky, Kyiv, 7, 34.

Prasolov, V. V. (1996). Zadachi i teoremy linejnoj algebry. Moscow: Nauka, 304.

Zinchuk, M. O., Novytskyy, V. V. (2005). Investigation of the Lyapunov equation for discrete almost conservative systems. Analitychni doslidzhennia modelei mekhanichnykh system. Zbirnyk prats Instytutu matematyky Natsionalnoi akademii nauk Ukrainy, 8, 1–26.

Teteriatnyk, O.V. (2014). Analytic expression of optimal control for systems of two coupled controllable almost conservative oscillators. Zbirnyk prats Instytutu matematyky Natsionalnoi akademii nauk Ukrainy, 11 (5), 231–239.

Gantmaher, F. R. (2010). Matrix theory. Moscow: fizmatlit, 560.

Lankaster, P. (1973). Matrix theory. Moscow: Nauka, 280.

Horn, R. A., Johnson, C. R. (2012). Matrix analysis. Cambridge university press, 643.




DOI: http://dx.doi.org/10.21303/2461-4262.2017.00354

Refbacks

  • There are currently no refbacks.




Copyright (c) 2017 Olena Teteriatnyk

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

ISSN 2461-4262 (Online), ISSN 2461-4254 (Print)