Novel Stability Criteria of Cyber-physical Microgrid Systems via Adjustable-parameter-square-dependent Mixed Convex Combination

An open network with low-bandwidth communication channels is applied to support the information exchange in the cyber-physical microgrid system, making the load frequency control (LFC) subject to inherent time-varying delay. In the stability analysis for delayed microgrid systems with LFC scheme, it is crucial to estimate reciprocally convex and quadratic polynomial function terms on the time-varying delay in the Lyapunov-Krasovskii functional (LKF) derivative for obtaining less conservative stability criteria. In this paper, an adjustable-parameter-square-dependent mixed convex combination strategy is proposed, in which
$\alpha ^{2}$
-dependent reciprocally convex combination lemma introduces some
$d^{2}(t)$
terms into the LKF derivative, and
$\beta ^{2}$
and
$M^{2}$
-dependent quadratic convex combination lemma relaxes the negativeness condition of the quadratic polynomial function with greater freedom. Based on the augmented LKF and mixed convex combination approaches, more relaxed stability criteria are derived. Finally, simulation examples are given to verify the generality of the proposed method and its superiority in stability analysis of microgrid systems.