• Dmitry AltshullerEmail author
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 432)


This chapter lays the foundations for subsequent investigations. The problem of absolute stability is formulated using the language of integral equations and the most general form of the nonlinear block. Then the so-called quadratic criterion for absolute stability is stated and proved. This criterion, in turn, relies on the concept of minimal stability and the so-called delay-integral-quadratic constraints. A criterion for minimal stability is stated and proved. In the last section, two integral inequalities, which will play a crucial role in derivation of the delay-integral-quadratic constraints, are also stated and proved.


Integral Inequality Absolute Stability Hermitian Form Volterra Integral Equation Quadratic Constraint 
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Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  1. 1.Parker AerospaceRiversideUSA

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