Delay-Dependent Stability Criteria for Networked Microgrid Load Frequency Control Systems via Variable-Augmented Free-Weighting Matrices

This paper investigates the delay-dependent stability problem of cyber–physical microgrid load frequency control (LFC) systems subject to time-varying communication delays. In the considered microgrid framework, renewable energy sources, hybrid energy storage units and the microgrid central controller are connected through an open communication network, which inevitably introduces time-varying delays into the closed-loop LFC system. To estimate the maximum admissible upper bound (MAUB), the variable-augmented free-weighting-matrix stability criterion is applied to the delayed microgrid system. To avoid the additional treatment of delay-dependent quadratic matrix terms, selected integral quantities are retained as augmented variables, and their intrinsic relationships are incorporated through zero-equality constraints with free-weighting matrices. Consequently, quadratic and higher-order terms with respect to the time-varying delay are prevented from arising in the derivative of the Lyapunov–Krasovskii functional (LKF). By employing the constructed LKF together with augmented-variable free-weighting matrices, novel delay-dependent stability conditions are obtained, which are expressed in the form of linear matrix inequalities (LMIs). Finally, numerical comparisons and time-domain simulations are provided to demonstrate the effectiveness of the adopted criterion in estimating the allowable communication-delay margin. Numerical results show that the proposed method obtains larger admissible communication-delay margins than existing criteria, demonstrating reduced conservatism.