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This paper has proposed a new energy based switching scheme for controlling dc-dc buck converter circuits and analysed its stability. There are three modes of operations, and the switching among these three modes depends on the reference voltage and the inductor reference current. The inductor reference current is calculated by the principle of energy balance. The reference voltage is designed to ensure that the voltage ripple as well as average value of the output voltage remain approximately constant in response to line and load disturbances. The phase plane analysis and sensitivity matrix analysis show that the proposed control scheme is free from chaos and infact has a super-stable orbit.

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This paper has proposed a new switching scheme for controlling de-dc boost converter circuits and presented the stability analysis by using the method of multiple Lyapunov functions. The dc-dc hwst converter is modeled to operate in three modes of operations. The switching among these three modes depends on capacitor output voltage and inductor peak current. The inductor peak current is calculated from the basic principle of energy balance. Whatever energy is lost by the capacitor to the load, the same amnunt of energy has to he gained by the inductor. The minimum load resistance is also calculated to determine the maximum energy transfer to the load. The stability of this scheme is analyzed in the phase plane and the stability of the limit cycle is established by using multiple Lyapunov functions. In particular, it is shown that state trajectories in the phase plane reach a stable limit cycle and remain there. Different Lyapunov functions are defined for different modes that are shown to be positive and decreasing whenever the corresponding mode is active. The simulation results demonstrate the performance of the proposed scheme under various load conditions and sudden input and load disturbances. Stability nf the limit cycle is established analytically and illustrated through the simulation results