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

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

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 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

Formation of required transfer zero location in the multiconnected dynamic system

A method for providing the required location of a transfer zero set in the linear multiconnected dynamic system with an equal number of inputs and outputs is considered. © Allerton Press, Inc. 2008

Minimax optimization of entanglement witness operator for the quantification of three-qubit mixed-state entanglement

We develop a numerical approach for quantifying entanglement in mixed quantum states by convex-roof entanglement measures, based on the optimal entanglement witness operator and the minimax optimization method. Our approach is applicable to general entanglement measures and states and is an efficient alternative to the conventional approach based on the optimal pure-state decomposition. Compared with the conventional one, it has two important merits: (i) that the global optimality of the solution is quantitatively verifiable, and (ii) that the optimization is considerably simplified by exploiting the common symmetry of the target state and measure. To demonstrate the merits, we quantify Greenberger-Horne-Zeilinger (GHZ) entanglement in a class of three-qubit full-rank mixed states composed of the GHZ state, the W state, and the white noise, the simplest mixtures of states with different genuine multipartite entanglement, which have not been quantified before this work. We discuss some general properties of the form of the optimal witness operator and of the convex structure of mixed states, which are related to the symmetry and the rank of states

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

Linear spaces on the intersection of cubic hypersurfaces

Upper bounds for the number of variables necessary to imply the existence of an m -dimensional linear variety on the intersection of r cubic hypersurfaces over local and global fields are given.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41633/1/605_2006_Article_BF02349626.pd

Assigning the set of zeros in control systems with parallel compensation

The problem of ensuring a given set of zeros in a linear multivariable dynamical system with the equal number of inputs and outputs that includes a parallel compensator and feedback loop is considered. Methods reducing this problem to the control of eigenvalues of a certain matrix are proposed; the simultaneous assignment of poles and zeros is reduced to the control of poles of two plants using a single controller. The calculations are based on well-known and well-tested modal control techniques. © 2013 Pleiades Publishing, Ltd

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