Parametrized Matrix Inequalities in Analysis of Linear Dynamic Systems
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Problems that can be reduced to polynomial and parametrized linear matrix inequalities are considered. Such problems arise, for example, in control theory. Well-known methods for their solution based on a search for nonnegative polynomials scale poorly and require significant computational resources. An approach based on systematic transformations of the problem under study to a form that can be addressed with simpler methods is presented.
Keywords:matrix inequalities nonconvex programming global optimization control theory 2D systems.
The author thanks P.V. Pakshin for valuable comments.
- 3.G. Chesi and R. H. Middleton, “ H∞ and H2 norms of 2-D mixed continuous-discrete-time systems via rationally-dependent complex Lyapunov functions,” IEEE Trans. Autom. Control 60 (10), 2614–2625 (2015).Google Scholar
- 6.V. V. Pozdyayev, “Atomic optimization. Part 1: Transformation of the search space and one-dimensional problems,” Upr. Bol’shimi Sist., No. 36, 39–80 (2011).Google Scholar
- 7.V. V. Pozdyayev, “Atomic optimization. Part 2: Multidimensional problems and polynomial matrix inequalities,” Upr. Bol’shimi Sist., No. 43, 95–123 (2013).Google Scholar
- 8.V. Posdyayev, “On evaluating H∞ and H2 performance of uncertain systems,” Proceedings of the 21st International Conference on Methods and Models in Automation and Robotics (MMAR) (IEEE, 2016), pp. 1217–1222.Google Scholar
- 10.V. V. Pozdyayev, “Necessary Conditions for 2D systems’ stability,” Preprints of the 1st IFAC Conference on Modeling, Identification, and Control of Nonlinear Systems (2015), pp. 800–805.Google Scholar
- 11.S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Studies in Applied Mathematics (Soc. Ind. Appl. Math., 1994).Google Scholar
- 15.G. Chesi and R. H. Middleton, “Static feedback design for 2D mixed continuous-discrete-time systems via LMIs,” Proceedings of European Control Conference (ECC) (2015), pp. 2859–2864.Google Scholar