Abstract
We present efficiently verifiable sufficient conditions for the validity of specific NP-hard semi-infinite systems of semidefinite and conic quadratic constraints arising in the framework of Robust Convex Programming and demonstrate that these conditions are “tight” up to an absolute constant factor. We discuss applications in Control on the construction of a quadratic Lyapunov function for linear dynamic system under interval uncertainty.
The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-0-387-35699-0_19
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Keywords
- Linear Matrix Inequality
- Interval Uncertainty
- Linear Dynamic System
- Robust Counterpart
- Quadratic Lyapunov Function
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© 2003 IFIP International Federation for Information Processing
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Ben-Tal, A., Nemirovski, A. (2003). On Approximate Robust Counterparts of Uncertain Semidefinite and Conic Quadratic Programs. In: Sachs, E.W., Tichatschke, R. (eds) System Modeling and Optimization XX. CSMO 2001. IFIP — The International Federation for Information Processing, vol 130. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35699-0_1
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DOI: https://doi.org/10.1007/978-0-387-35699-0_1
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