In this paper, the design of sliding mode controller for a singular biological economic model with a stage structure and uncertain parameters is studied. First, a biological economic system with uncertain parameters for the invasion of alien species is modeled by a singular system. Then, according to the theory of the T-S fuzzy system, an uncertain T-S fuzzy singular model is established and the stability of the model at the positive equilibria is discussed. Furthermore, a fuzzy integral sliding surface and a sliding mode controller are designed for the T-S fuzzy singular system with an uncertain term. At the same time, the state trajectories can be driven onto the integral sliding surface in finite time and a sufficient condition about the global asymptotic stability of sliding motion is obtained. Finally, a simulation is given to verify the effectiveness of the obtained results. INDEX TERMS The invasion of alien species, Positive equilibria, sliding mode controller, global asymptotic stability.

With the increase of the renewable energy penetration (REP) level in the interconnected power grid, the proportion of the grid-connected conventional synchronous generators reduces continuously, resulting in the decrease of the system inertia. The insufficient system inertia brings challenges to the system frequency stability. Battery energy storage systems (BESSs), regarded as the high-quality frequency regulation resource, play an important role in maintaining the frequency stability of the system with the high REP level. To configure the proper power of BESSs in system frequency regulation, a BESS power configuration scheme (PCS) considering the REP constraint is proposed in this paper. In particular, the process to obtain the REP boundary of the interconnected grid on the premise of system frequency stability is included in the PCS, and the optimal power configuration of the BESS is further determined on the analysis of the BESS impact on the REP boundary. Furthermore, a simulation model of the Australian five-area interconnected power grid is built in MATLAB/Simulink, and the proposed REP-constrained PCS is verified and analyzed. At last, the promising results show that the PCS can take full advantages of the BESS in frequency regulation and meet the system requirement of the frequency stability at a particular REP level.

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