Control and Informatics Div.

Bitola, Macedonia

Control and Informatics Div.

Bitola, Macedonia
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Stefanovski J.,Control and Informatics Div.
Systems and Control Letters | Year: 2011

We present a numerical algorithm to solve a discrete-time linear matrix inequality (LMI) and discrete-time algebraic Riccati system (DARS). With a given system (A,B,C,D) we associate a para-hermitian matrix pencil. Then we transform it by an orthogonal transformation matrix into a block-triangular para-hermitian form. Under either of the two assumptions (1) matrix pair (A,B) is controllable or (2) matrix pair (A,B) is reachable and (A,B,C,D) is a left invertible system, we extract the solution of LMI and DARS by the entries of the orthogonal transformation matrix. © 2010 Elsevier B.V.


Stefanovski J.,Control and Informatics Div.
International Journal of Robust and Nonlinear Control | Year: 2013

We generalize the J-spectral factorization of para-Hermitian proper rational matrix in the case when it has no constant inertia on the imaginary axis. This result and the presented numerical algorithm are based on a canonical form of para-Hermitian matrix pencils. We apply the new spectral factorization to the optimal control of the proper plant by dynamic measurement feedback over a frequency region. Copyright © 2012 John Wiley & Sons, Ltd. Copyright © 2012 John Wiley & Sons, Ltd.


Stefanovski J.,Control and Informatics Div.
International Journal of Robust and Nonlinear Control | Year: 2010

Necessary and sufficient conditions for the existence of a minimizing discrete-time ℋ2 control, when assumptions are the internal stabilizability and left- and right-invertibility of transfer matrices G 12 and G21, are presented. Unlike the existing approach with a transformation into a disturbance decoupling problem with a measurement feedback and internal stability, we use a direct approach: from frequency to time domain. The first main result gives a necessary and sufficient existence condition for ℋ2 control: that a minimal realization of the infimal controller is stabilizing. The second main result presents a realization of an optimal controller that has a state observer form, identical to the form of the regular case, except that the state-feedback gain matrix and the observer gain matrix are replaced by some stabilizing matrices. Copyright © 2009 John Wiley & Sons, Ltd.


Stefanovski J.,Control and Informatics Div.
Systems and Control Letters | Year: 2014

For a given descriptor realization of para-hermitian rational matrix Π(s), we present a generalization of Kalman-Yakubovič-Popov lemma, i.e. necessary and sufficient conditions for Π ≥0 on the imaginary axis, in terms of an inequality with constant matrices. The result is quite general, since Π can have poles and zeros on the extended imaginary axis, hence the nonstrict inequality Π(jω) ≥0, ωR can hold, instead of the strict inequality. Π can be singular. The descriptor realization is required to be only impulse controllable and controllable (or stabilizable and detΠ≈0). A spectral factorization of Π is given, by the above mentioned constant matrices. Three consequences of the generalized KYP lemma, and an illustrative numerical example are given. © 2014 Elsevier B.V. All rights reserved.


Stefanovski J.D.,Control and Informatics Div.
Kybernetika | Year: 2012

We show how we can transform the ℋ∞ and ℋ2 control problems of descriptor systems with invariant zeros on the extended imaginary into problems with state-space systems without such zeros. Then we present necessary and sufficient conditions for existence of solutions of the original problems. Numerical algorithm for ℋ ∞ control is given, based on the Nevanlinna-Pick theorem. Also, we present an explicit formula for the optimal ℋ2 controller.


Stefanovski J.D.,Control and Informatics Div.
Systems and Control Letters | Year: 2013

We transform an H∞ control problem with invariant zeros on the extended imaginary axis into a regular problem. Then using the Nevanlinna-Pick theorem, we find necessary and sufficient existence conditions for the original H∞ control problem. An algorithm and examples with invariant zeros on the extended imaginary axis are given. By the same approach, we also solve the singular H2 control problem. © 2013 Elsevier B.V. All rights reserved.

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