This paper proposes novel multi-energy inertia support for simultaneous frequency and voltage control of an isolated hybrid power system (IHPS). Multi-energy storage (gas inertia – hydrogen storage, thermal inertia – solar thermal storage, hydro inertia – gravity hydro storage, chemical inertia – battery energy storage) supported by demand side management (DSM) for simultaneous voltage and frequency regulation and backed by biodiesel generators, are the essential elements of IHPS. A novel control strategy of concurrent virtual droop control, virtual damping control, virtual inertia control, and virtual negative inertia control is proposed to utilise multiple inertia sources and to improve LFC and AVR performance effectively. The effective coordination of inertia sources in eradicating oscillations in IHPS, is aided by a developed cascaded proportional integral-tilt-integral-sliding mode (PI-TISMC) controller. The performance of PI-TISMC is compared with PID, PI-PID, and PI-SMC controllers. A maiden attempt has been done by training five diverse classes of optimization techniques to optimize the parameters of controllers in the present work. The results are evaluated in MATLAB and it is evident from the results that the performance of frequency control is improved by 6.5%, 7.8% and 3.4 s (over shoot, undershoot, and settling time). The performance of frequency control is improved by 6.5%, 7.8% and 3.4 s (over shoot, undershoot, and settling time). Similarly, the performance of voltage control is improved by 6.7%, 4.8% and 2.3 s (over shoot, undershoot, and settling time) by employing developed PI-TISMC controller and proposed concurrent inertia control. The combination exhibits superior performance in minimizing oscillations in IHPS due to variations in loading and solar insolation.