Your schematic appears to apply a modified sine wave to a series LC. I've played with similar simulations in a hope to find an easy way to regulate voltage. I found a problem because the LC tries to continue resonating as current is abruptly shut off. Even when it's only an inductor, it wants to continue pulling current at shut-off through all neighboring components. If no freewheeling diode (mosfet, snubber network, etc.) is installed then the inductor generates unwanted high voltage spikes.
It may be more effective if you gate the H-bridge so that it applies plain AC square waves. Do you want to sense the resonant frequency of your LC combo? Then install a low-ohm resistor in series. This allows you to sense each zero crossing of current at the exact time when current falls to zero. That is the cue to change the state of your H-bridge.