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July  2013, 9(3): 579-593. doi: 10.3934/jimo.2013.9.579

On the robust control design for a class of nonlinearly affine control systems: The attractive ellipsoid approach

 1 Department of Control and Automation, CINVESTAV, Av, Instituto Politecnico Nacional 2508, Mexico D.F., Mexico, Mexico, Mexico

Received  September 2011 Revised  October 2012 Published  April 2013

This paper is devoted to a problem of robust control design for a class of continuous-time dynamic systems with bounded uncertainties. We study a family of nonlinearly affine control systems and develop a computational extension of the conventional invariant ellipsoid techniques. The obtained method can be considered as a powerful numerical approach that makes it possible to design a concrete stabilizing control strategies for the resulting closed-loop systems. The design procedure for this feedback-type control is based on the classic Lyapunov-type stability analysis of invariant sets for the given dynamic system. We study the necessary theoretic basis and propose a computational algorithm that guarantee some minimality properties of the stability/attractivity regions for dynamic systems under consideration. The complete solution procedure contains an auxiliary LMI-constrained optimization problem. The effectiveness of the proposed robust control design is illustrated by a numerical example.
Citation: Vadim Azhmyakov, Alex Poznyak, Omar Gonzalez. On the robust control design for a class of nonlinearly affine control systems: The attractive ellipsoid approach. Journal of Industrial & Management Optimization, 2013, 9 (3) : 579-593. doi: 10.3934/jimo.2013.9.579
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