Small power system networks, integrated with renewable energy resources, often pose several technical challenges to maintain the system frequency due to insufficient inertia in the network. To overcome these challenges, the present study proposes a Lyapunov based controller to emulate the inertia which would effectively support the frequency under generation-demand imbalance conditions in a mixed generation system. The parameters of the controller are optimally selected using the Comprehensive Learning Particle Swarm Optimisation (CLPSO) algorithm and the stability conditions of the controller are established and proved using Lyapunov stability criteria. The proposed controller is implemented in MATLAB/SIMULINK considering a 4-bus mixed generation power system network consisting of a single synchronous, diesel and DFIG-based wind generator. The results of the simulation convincingly demonstrate that the proposed inertia emulation controller could support the frequency of the mixed power system under generation-demand imbalance conditions.