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1 year ago in Robotics By Natasha

How can one check the positive definiteness of a non-quadratic function‑ Please suggest relevant papers.

How is positive definiteness assessed for functions that are not quadratic? Could you recommend relevant literature on this topic?

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By Vipul Answered 3 months ago

Proving positive definiteness for non-quadratic functions often involves showing the function is bounded below by a known positive definite function. For polynomial functions, Sum-of-Squares (SOS) programming is a powerful method. Relevant literature includes Parrilo's seminal work on SOS techniques (2000) and standard nonlinear systems texts like "Nonlinear Systems" by Khalil, which discuss constructing Lyapunov functions—a common context for this problem in control.

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