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A new D-stability area for linear discrete-time systems

Krokavec Dušan, Filasová Anna

Archives of Control Sciences

2019

Vol. 29, No. 1

5--23

The paper addresses the problem of constrained pole placement in discrete-time linear systems. The design conditions are outlined in terms of linear matrix in equalities for the D-stable ellipse region in the complex Z plain. In addition, it is demonstrated that the D-stable circle region formulation is the special case of by this way formulated and solved pole placement problem. The proposed principle is enhanced for discrete-time linear systems with polytopic uncertainties.

Off-line robustification of Generalized Predictive Control for uncertain systems

Otmane K. K., Bali N., Nezli L.

Archives of Control Sciences

2014

Vol. 24, no. 4

499--513

An off-line methodology was proposed for enhancing the robustness of an initial Generalized Predictive Control (GPC) by convex optimization of the Youla parameter. However, this procedure of robustification is restricted with the case of the systems affected only by unstructured uncertainties. This paper proposes an extension of this method to the systems subjected to both unstructured and structured polytopic uncertainties. The main idea consists in adding supplementary constraints to the optimization problem which validates the Lipatov stability condition at each vertex of the polytope. These polytopic uncertainties impose a set of non convex quadratic constraints. The globally optimal solution is found by means of the GloptiPoly3 software. Therefore, this robustification provides stability robustness towards unstructured uncertainties for the nominal system, while guaranteeing stability properties over a specified polytopic domain of uncertainties. Finally, an illustrative example is given.