Leonid Lyubchyk, Olga Kostyuk


The problem of disturbance rejection in multivariable control systems is considered. It has been shown that different two-degree-of-freedom control structures used for immeasurable disturbance estimation and compensation may be treated as a particular case of a general Inverse Model Control approach. The decomposition of the problem into the separate disturbance estimation and compensation is suggested. Moreover the connection between inverse model design problems and unknown input observer theory has been established in order to give a practical way to inverse model parameterization and design. The properties of closed-loop selective invariant control system with model-based controllers have been also investigated with the aim of attainable accuracy estimation.


disturbance rejection; inverse model; invariance; model-based control; unknown-input observers

Full Text:



Francis, B. (1987). A course of H control theory. Lecture Notes in Control and Information Sciences. Berlin: Springer – Verlag.

Hou, M., & Muller, P.C. (1992). Design of observers for linear systems wits unknown inputs. IEEE Trans. on Automatic Control, 37, 871-875.

Kelmans, G.K., Poznyak, A.S., & Chernitser, A.V. (1981). Adaptive locally optimal control. Int. J. System Science, 12, 2, 235-254.

Kostenko, Yu.T., & Lyubchik, L.M. (1996). Dynamic model-based control systems. (in Russian). Kharkov: Osnova.

Kurek, J.T. (1982). Observation of the state vector of linear multivariable systems with unknown input. Int. J. of Control, 36, 511-515.

Lyubchik, L.M. (1995). Inverse model control and sub-invariance in linear discrete multivariable systems. Proc. of the 3-rd European Control Conf., Roma, 4, 2, 3651-3659.

Lyubchyk L.M. (2011). Disturbance Rejection in Linear Discrete Multivariable Systems: Inverse Model Approach. Proceedings of 18th IFAC World Congress, Milan, Italy.

Morari, M., & Zafirov, E. (1989). Robust processes control. New Jersey: Prentice Hall.

Seraji, H. (1989). Minimal inversion, command tracking and disturbances decoupling in multivariable systems. Int. J. of Control, 49, 2093-2191.

Silverman, L.M. (1969). Inversion of multivariable linear systems. IEEE Trans. on Automatic. Control, 14, 270-276.

Tsypkin, Ya. Z., & Holmberg, U. (1995). Robust stochastic control and internal model control. Int. J. of Control, 61, 4, 809-822.

Wolovich, W.A. (1995). Automatic Control Systems: Basic Analysis and Design, Philadelphia, PA: Saunders.


  • There are currently no refbacks.

Copyright (c) 2015 Leonid Lyubchyk, Olga Kostyuk

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

ISSN (Print) : 2449-7320

ISSN (Online) : 2449-8726