Calculation of decoupling zeroes in the multiconnected dynamic system

A recursive method for calculating decoupling zeroes in the linear multiconnected dynamic system based on the application of matrix canonization techniques is proposed. Its essence is that the problem dimension is successively decreased and reduced to finding eigenvalues of some matrix. The results obtained can be used to check controllability and observability as well as to calculate uncontrollable and unobservable modes of the dynamic system. © Allerton Press, Inc., 2010

Problems of improper dynamic system analysis and synthesis with regard for transfer zeroes

The notion of a transfer zero as applied to improper dynamic systems is considered. An algorithm that makes it possible to reduce the calculation of improper system zeroes to finding ordinary system zeroes is presented. A method for providing the specified position of a transfer zero set in the improper dynamic system having an equal number of inputs and outputs is proposed. © Allerton Press, Inc. 2009

Analytical synthesis of functional observers for systems with signal perturbations

© 2014, Allerton Press, Inc. An algorithm for the analytical synthesis of functional observers is proposed which is based on a nondegenerate transformation of a state vector using the technology of matrix canonization and methods for solving linear matrix equations of arbitrary dimension. Conditions of the solvability of the synthesis problem and the invariance of the constructed observer to signal perturbations in the form of a system of linear matrix equations are formulated

Analytical synthesis of a functional observer of the state of a bilinear dynamic system

© 2017, Allerton Press, Inc. The problem of asymptotic estimation of a linear combination of the state variables of a bilinear dynamic system using a minimum-order observer is considered. An algorithm for calculating the matrix coefficients of a functional observer using the technology of canonization of matrices is proposed, and solvability conditions for synthesis problem are derived

Estimation of directly unmeasurable external perturbations using functional observers

© 2015, Allerton Press, Inc. It is shown that the problem of estimating unmeasurable external perturbations from a mathematical point of view is equivalent to estimating some of the state variables of an extended plant. An algorithm for estimating unmeasurable external perturbations using a functional observer is proposed, and conditions for the solvability of the synthesis problem are formulated. The resulting solution is obtained using the method of matrix canonization

Synthesis of input/output matrices for a multi-input multi-output dynamical system by given zeros of transfer matrix

The problem of synthesizing a linear multi-input multi-output dynamical system with equal numbers of inputs and outputs that has given transfer zeros is solved by applying the matrix canonization technique. Algorithms for constructing input and output matrices of the dynamical system model ensuring given location of transfer (system) zeros are proposed. © 2008 Pleiades Publishing, Ltd

Analytical synthesis of functional low-order observers

© 2015, Pleiades Publishing, Ltd. Simultaneous estimation of several linear combinations of the state variables of a multiple input–multiple output dynamical system is considered. A method for decomposing the state vector into several components is proposed such that only some of these components are needed to reconstruct the desired vector function. An algorithm for the analytical synthesis is described that yields a functional observer of the minimum possible order. The procedure for computing the observer coefficients is reduced to a modal control problem. The proposed method is based on the matrix canonization technique

Analytical synthesis of physically implementable controllers for multivariable objects using the embedding technique

It is shown that the problem of synthesis of control systems (with a reference model) for a multivariable dynamic object can be solved exactly using the embedding technique. The synthesis algorithm presented provides stability and physical implementation of the solution obtained. © 2012 Allerton Press, Inc

Analytical synthesis of invariant reduced-order state observers

An algorithm for the analytical synthesis of reduced-order observers for dynamic systems with an output matrix of arbitrary form is proposed, and invariance conditions for the constructed observer with respect to external disturbances are formulated. Solvability conditions for the synthesis problem are obtained in the form of a system of linear matrix equations. The proposed algorithm is based on a nondegenerate transformation of the state vector using the matrix canonization technique and methods for solving linear matrix equations of arbitrary dimension. © 2013 Allerton Press, Inc

Analytical synthesis of functional observers

A technique for constructing the observers to evaluate a linear combination of state variables is considered. We propose an algorithm for analytical synthesis of the minimum-order functional observers based on the nondegenerate transformation of the object model in the state space using the matrix canonization technology. The applicability limits of the technique and the conditions of problem solvability are defined. © 2013 Allerton Press, Inc