In this article, the power fluctuation problem caused by adding renewable energy sources to microgrids (MGs) is addressed. These power fluctuations which can cause several adverse effects, including system instability, load shedding, and eventually blackouts are attenuated by designing a load frequency controller (LFC) to provide a constant and uniform frequency in different operation cases of MGs. This article designs a dynamic output feedback controller (DOFC) for LFC in MGs while considering the contraction observer for attack mitigation. We suggest a new formulation of the sufficient conditions for the DOFC design problem in the form of bilinear matrix inequalities (BMIs) and try to minimize the frequency deviation subject to load, solar, and wind energy changes. The proposed formulation effectively changes the problem to a new BMI model which can easily be divided into two problems, one is a convex optimization problem and the remained part is a quadratic matrix inequality problem which is linearized around the feasible solution of the linear matrix inequality part by a Taylor-like expansion. This leads to a more exact and less conservative solution as compared to the previous methods suggested in the literature. To illustrate the merits of the developed approach, numerical simulations on a sample ac&#x2013;MG are carried out. Comparing norms of the frequency variations in the closed-loop system with multiple prominent methods in previous works, including <formula><tex>${{\bm{H}}_\infty },{\bm{\ \mu }}$</tex></formula>, fuzzy type-1, and intelligent-PI, shows that our proposed method reduces the two and infinity norms of frequency fluctuations by 84&#x0025; and 80&#x0025;, respectively compared to the traditional <formula><tex>${{\bm{H}}_\infty }$</tex></formula> method which is the best among the analyzed approaches. This further verifies the efficacy of the designed DOFC in our article.