The absolute stability problem of single-input single-output Lur’e systems with uncertain feedback belonging to a sector bounded by possibly asymmetric piecewise linear characteristics is considered. These characteristics determine a state space partition into slabs. Sign conditions of quadratic functions and quadratic forms constrained to the slabs are reformulated in terms of cone-constrained linear matrix in- equalities. It is shown that these conditions can be solved by defining a suitable copositive programming. Copositivity is then exploited in order to determine a sufficient condition for the existence of a piecewise quadratic Lyapunov function which is used to get an absolute stability result for the Lur’e system. An example with asymmetric sector bounds shows the effectiveness of the the proposed approach.

Cone-copositivity for Absolute Stability of Lur’e Systems

Vasca F.
2014

Abstract

The absolute stability problem of single-input single-output Lur’e systems with uncertain feedback belonging to a sector bounded by possibly asymmetric piecewise linear characteristics is considered. These characteristics determine a state space partition into slabs. Sign conditions of quadratic functions and quadratic forms constrained to the slabs are reformulated in terms of cone-constrained linear matrix in- equalities. It is shown that these conditions can be solved by defining a suitable copositive programming. Copositivity is then exploited in order to determine a sufficient condition for the existence of a piecewise quadratic Lyapunov function which is used to get an absolute stability result for the Lur’e system. An example with asymmetric sector bounds shows the effectiveness of the the proposed approach.
978-1-4673-6088-3
Lur'e systems; cone-copositivity; Lyapunov method
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.12070/11563
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