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.
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