ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Analysis and Synthesis of Dynamic MIMO-system Based on Band Matrices of Special Type


Evgeny Anatolievich Mikrin

RAS Acad., Dr. Sci. (Eng.), Professor
General Designer
First Deputy General Director at PSC Korolev RSC "Energia"
141070, Moscow region, Korolev, Lenin Street, Building 4a)

Vladimir Nikolaevich Ryabchenko

Dr. Sci. (Phys.-Math.), Associate Professor
Senior Technologist of JSC "RDC at FGC of UES"
115201, Moscow, Kashirskoe highway, House 22, Building 3
Professor of Dep. "Automatic Control Systems" at Bauman MSTU
Russia, 105005, Moscow, 2-nd Bauman Street, House 5

Nikolay Evgenievich Zubov

Dr. Sci. (Eng.), Professor
Professor of Dep. "Automatic Control Systems",
Dean of "Rocket and Space Techniques" faculty at Bauman MSTU
105005, Moscow, 2-nd Bauman Street, Building 5

Alexey Vladimirovich Lapin

Senior Lecturer of Dep. "Automatic Control Systems" at Bauman MSTU
Russia, 105005, Moscow, 2-nd Bauman Street, Building 5


The problem of analysis and synthesis of linear controllable dynamic MIMO-systems (systems with multiple input and multiple output) using band matrices of special type is considered. The fundamental basis of suggesting approach is A.N. Krylov transformations (Krylov subspaces). The main matrix transformations applying for getting solutions are left and right zero divisors. Band matrices of special type with properties that uniquely define the property of full controllability are formed basing on mentioned transformations for linear fully controllable MIMO-system. Besides, these matrices allow analytic connecting parameters of controllable MIMO-system and coefficients of its characteristic polynomial. Obtaining the formula of this connection is founded on the well-known relationship between MIMO-system controllability matrix and the companion (canonical) Frobenius form for its characteristic polynomial. Using the obtained formula a controller is synthesized with feedback providing coefficients of characteristic polynomial of the closed-loop controlled MIMO-system matching the assigned coefficients. In simplified form (for single input systems) the formula of controller is similar to the well-known Bass – Gura and Ackermann formulas. The condition is obtained for parameterizing the set of controllers that provide the assigned characteristic polynomial of closed-loop MIMO-system and that are generated by left zero divisor of a band matrix of special type.



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