JP Strezevo

Bitola, Macedonia

JP Strezevo

Bitola, Macedonia
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Stefanovski J.,JP Strezevo
Optimal Control Applications and Methods | Year: 2011

We present a structure-preserving numerical algorithm, based on using orthogonal matrices, and sufficient conditions for LQ control of rectangular descriptor systems. The sufficient conditions are quite general: stabilizability, impulse controllability, generalizations of detectability and impulse observability. The solution in the case of wide descriptor system differs from the solution of tall descriptor system. Copyright © 2010 John Wiley & Sons, Ltd.


Stefanovski J.D.,JP Strezevo
IEEE Transactions on Automatic Control | Year: 2011

We reconsider the singular control problem with marginal stability of the closed loop system, when the transfer matrix from the input to the output can have linearly dependent columns, and zeros on the extended imaginary axis. We present a new theoretical (existence) result and a new numerical algorithm, based on finding an orthogonal transformation of the matrix pencil associated to the Euler-Lagrange differential equations into a block-triangular form. We present an application in linear quadratic control of descriptor systems, under the constraints of physical realizability of the control and impulse-free and marginally stable closed-loop system. © 2006 IEEE.


Stefanovski J.D.,JP Strezevo
International Journal of Control | Year: 2010

This article presents a general formula for discrete-time ℋ2 control. It works with the regular and singular case of ℋ2 control, i.e. in the case of possibly non-left-invertible matrices G12 and non-right-invertible matrices G21, with possible unit circle invariant zeros. In the generic case, it can be simplified and adapted to work with the plant transfer matrix directly, without invoking the matrices of the parameterisation of stabilising controllers. A further result of this article is the presented necessary and sufficient conditions for state-space ℋ2 control, under only stabilisability and detectability assumptions. If the conditions are satisfied, an observer-based ℋ2 controller is constructed. The corresponding numerical algorithm consists of solving two discrete-time algebraic Riccati systems (DARSs) and two eigen-problems. © 2010 Taylor & Francis.


Stefanovski J.D.,JP Strezevo
International Journal of Control | Year: 2012

We present algorithms for optimal harmonic disturbance attenuation in standard discrete-time control structure, based on a parametrisation of (marginally) stabilising controllers. The Frobenius norm and the spectral norm of the closed-loop transfer matrix at the disturbance frequencies are minimised. If there is only one frequency of the disturbance, the controller has an observer-based form, which we obtain by solving a static output feedback (SOF) stabilisation control problem. Although the SOF stabilisation problem is hard, the generical case of nonsquare matrix G 22 is solved by linear algebra methods. Numerical simulation results are presented. As a corollary, we transform the control problem with unit circle invariant zeros into a ℋ ∞ control problem without such zeros. The elimination of the unit circle invariant zeros is based on the fact that matrix Y(zI-A+BF) -1 is stable, where (Y,F) with Y≥0 is a solution of a discrete-time algebraic Riccati system. © 2012 Copyright Taylor and Francis Group, LLC.


Stefanovski J.,JP Strezevo
International Journal of Control | Year: 2010

Given a plant transfer matrix as a fraction of two polynomial matrices, we present a doubly coprime factorisation identity over the proper stable rational matrices of the plant transfer matrix, and apply it to compute a controller transfer matrix in H2 optimal control of discrete-time systems. If there are no uncontrollable modes of the plant transfer matrix, the controller is given by a fraction of two polynomial matrices, where the order of the denominator is less than or equal to the McMillan degree of the plant. © 2010 Taylor & Francis.


Stefanovski J.D.,JP Strezevo
IEEE Transactions on Automatic Control | Year: 2015

We present an algorithm for suboptimal ℋ∞ control of descriptor systems possessing invariant zeros on the imaginary axis and infinity. It is proved that the algorithm works also in an optimality case. The algorithm is illustrated by examples. © 2015 IEEE.


We formulate a matrix interpolation problem with existing interpolation points on the imaginary axis and infinity and existing equal left and right interpolation points, using the concept of parametrisation of stabilising controllers. Then, we solve the problem of obtaining all its solutions. If interpolation points at infinity are absent, we show that the introduced problem is equivalent to the existing one. We apply this result to solve the problem of optimal interpolation with existent interpolation points on the imaginary axis and infinity. We show by an example that the solution of optimal interpolation is directly applicable to the one-block optimal control with existent invariant zeros on the imaginary axis and infinity. It is seen from the example that not only the transfer matrix of the closed-loop system is constrained on the extended imaginary axis, but also its derivatives. © 2014 Taylor & Francis.


Stefanovski J.,JP Strezevo
International Journal of Control | Year: 2010

A spectral factorisation algorithm of improper matrices and existence results, under controllability conditions, are presented. Based on these results, an algorithm for linear-quadratic (LQ) control of rectangular descriptor systems without the detectability and infinite observability conditions is presented. The matrix pencil associated with the Euler-Lagrange differential equations can be singular, can have finite generalised eigenvalues on the imaginary axis and infinite generalised eigenvalues of any multiplicity. In the class of optimal state feedback controls, we find a control that renders the closed-loop system marginally stable and impulse-free. Also we find conditions on x(0-) that guarantee the optimality. It is shown how the disturbance attenuation problem of descriptor systems can be re-formulated as an optimal state feedback-feedforward control problem, for which the results of this article can be applied. When applied to state space systems, the algorithm of this article, which is based on using orthogonal matrices, solves the linear matrix inequality that is used in control theory, in its most general form. © 2010 Taylor & Francis.

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