Band Formulas for Analysis and Synthesis of Controlled Dynamic MIMO Systems

Authors: Zubov N.E., Mikrin E.A., Misrikhanov M.Sh., Ryabchenko V.N. Published: 23.05.2014
Published in issue: #3(96)/2014  

Category: Control Systems  
Keywords: matrix zero divisor, dynamical system, controllability, band criterion, state feedback, parameterization of regulators

The application of A.N. Krylov’s method in the control theory for solving various problems of analysis and synthesis of linear dynamic multi-input multi-output (MIMO) systems is discussed. These problems include the calculation of a balanced implementation of the linear MIMO system transfer matrix in the state space; reduction and decomposition of a model of this system in the state space; the definition of controlled and observed subspaces; stabilization using state elements feedback; synthesis of the control that provides the system invariance to the external perturbation. An approach is presented for analysis and synthesis of linear dynamical MIMO-systems on the basis of band formulas of controllability analysis. Using transformations of controllability band matrices, the band formula, connecting the MIMO-system parameters and the characteristic polynomial coefficients, is found.


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