Auxiliary‐function‐based double integral inequality approach to stability analysis of load frequency control systems with interval time‐varying delay

Abstract

A new approach is presented for the stability problem of one‐area and multi‐area load frequency control (LFC) scheme with time delays in this study. Novel stability criteria with delay dependency in terms of linear matrix inequalities for LFC systems are derived by an augmented Lyapunov–Krasovski functional with triple integral terms. The LFC design takes the interval time‐varying communication delays into account and the load disturbance is mathematically modelled as a norm‐bounded non‐linear function. This study suggests a new class of inequality for double integral of quadratic functions via intermediate auxiliary functions, which produce more tighter bounds than what Wirtinger's double integral inequality produces. Case studies are carried out to illustrate the validity of the proposed delay‐dependent proportional–integral‐based output feedback design method.