Abstract

PANTOJA, Andrés; MOJICA NAVA, Eduardo  and  QUIJANO, Nicanor. Sum of squares decomposition: controltheory and applications . Ing. Investig. [online]. 2010, vol.30, n.3, pp.57-70. ISSN 0120-5609.

Sum of squares decomposition (SOS) techniques allow us to use numerical methods, such as semidefinite programming, to prove positivity of multivariable polynomial functions. It is well known that it is not an easy task to find Lyapunov functions for stability analysis of nonlinear systems. In this work, we use an algorithmic tool to solve this problem. This approach is presented as SOS programming and solutions are obtained with a Matlab toolbox. We present simple examples of SOS concepts, stability analysis for nonlinear polynomial, and rational systems with uncertainties in the parameters to show the use of this tool. Besides of these approaches, we present an alternative stability analysis for switched systems with a polynomial approach.

Keywords : sum of squares; SOS; stability analysis; nonlinear systems; switched systems.

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