The importance of bounded real and positive real functions in the stability analysis of 2-D system

The necessary and sufficient conditions for the existence of positive definite solutions for the 2-D Lyapunov equation for 2-D discrete, 2-D continuous, and differential-delay systems are presented. It is shown that these conditions are related to the strictly positive real and strictly bounded real conditions. The relationship between these conditions and the stability ones is also discussed.<
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