Positivity of Complete Quadratic Lyapunov-Krasovskii Functionals in Time-Delay Systems
This chapter discusses positivity of quadratic functionals that arise in the stability analysis of time-delay systems. When both the single and double integral terms are positive, a necessary and sufficient condition for positivity is obtained using operator theory. This is applied to the Lyapunov-Krasovskii functional and its derivative. The coupled differential-difference equations are studied using the Sum-of-Squares (SOS) method.
KeywordsPolynomial Matrice Quadratic Inequality Quadratic Functional Small State Space Continuous Matrix Function
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