## 1 Introduction  
Reduction in operating switching frequency is an important requirement when implementing sliding mode control (SMC) for power electronic converters. An ideal SMC suggests that the switching frequency is high enough to consider the state variables are constant during a switching period and that the system's trajectories slide along a switching surface in such a way that the required dynamics are realized [1]. On the other hand, such a high switching frequency in a closed-loop control system causes substantial difficulty in calculating state variables known as chattering. In addition, it is also not feasible for practical power converters to operate at extremely high switching frequencies due to limitations of semiconductor power switches and added power loss. Chattering also causes poor control precision and high heat in power converters [2, 3]. In addition, the switching frequency has a considerable influence on the structural design of the converters since it directly impacts the size of inductors and capacitors as well as the switches themselves [1, 4]. Therefore, it is preferable to have an optimized and stable switching frequency. To nullify major drawbacks associated with the natural operation of the SMC and also to achieve a switching frequency, HM has been utilized by the scientific community since it offers some outstanding features such as simple implementation, generation of a switching signal without the need for a trigger signal, and no need for including a saturation function. In this method, the state trajectory is forced to move inside the region enclosed by constant or adaptive symmetric band values, which leads to reduced chattering and a narrow range of the switching frequency [1; 2; 5]. A satisfactory output voltage regulation with a smooth inductor current regulation have been achieved successfully [1; 4; 5]. Although it is an extremely effective technique, it unavoidably results in a time-varying switching frequency. High and time-varying switching frequencies result in steady-state errors, high switching losses, challenging output filter designs [5], EMI noises [3], and a reduction in the converters' capacity to regulate the voltage and current. Even though controlling the switching frequency is essential, it has not received as much attention in past research work. As a result, there are few similar investigations in the body of existing literature. As previously mentioned, there are a number of HM-based SMC studies in the literature, and research on this subject is accelerating at a high rate to provide appropriate transient and steady-state performance. Unfortunately, most HM-SMC investigations in the literature have concentrated solely on output voltage control [6; 7; 8; 9] or combination with inductor current control [10; 11; 12; 13; 14], disregarding variable switching frequency. To precisely address this need, the study in [4] presents a novel switching frequency controller based on the assumption of piecewise linear behavior of the sliding surface. The study formulates a new closed-loop control that measures the switching period, uses a frequency controller loop (FCL) to update the hysteresis band value, and drives the measured switching period to converge to a predetermined reference value. The outcomes show that both the switching frequency and state variables are effectively maintained at the reference levels, even during transitions. Because of its effectiveness, the FCL strategy has also been used with different sliding manifolds, such as fast terminal sliding surfaces [15]. Despite such improved outcomes of FCL, the technique necessitates a calibration for the other system variables as well as the switching frequency, adding computing complexity. The switching frequency calibration also gives a coefficient that has a considerable effect on the switching frequency, as shown in [15], as well as other system state variables, notably on the output voltage.