*Article* **Nonlinear Stabilization Controller for the Boost Converter with a Constant Power Load in Both Continuous and Discontinuous Conduction Modes**

**Juan Gerardo Parada Salado 1,† , Carlos Alonso Herrera Ramírez 2,† , Allan Giovanni Soriano Sánchez <sup>3</sup> and Martín Antonio Rodríguez Licea 3,\* ,†**


**Abstract:** The operation of Boost converters in discontinuous conduction mode (DCM) is suitable for many applications due to the, among other advantages, inductor volume reduction, high efficiency, paralleling, and low cost. Uses in biomedicine, nano/microelectromechanical, and higher power systems, where wide ranges of input/output voltage and a constant power load (CPL) can coexist, are well-known examples. Under extremely wide operating ranges, it is not difficult to change to a continuous conduction mode (CCM) operation, and instability, chaos, or bifurcations phenomena can occur regardless of the conduction mode. Unfortunately, existing control strategies consider a single conduction mode or linearized models because only slight resistive/CPL power level or input/output voltage variations (and no conduction mode changes) were expected. In this paper, new mathematical models for the Boost converter (with resistive or CPL) that are conduction mode independent are presented and validated. Since the open-loop dynamics of the proposed CPL model is unstable, a nonlinear control law capable of stabilizing the boost converter regardless of the conduction mode is proposed. A stability analysis based on a common-Lyapunov function is provided, and numerical and experimental tests are presented to show the proposal's effectiveness.

**Keywords:** constant power load; boost converter; discontinuous conduction mode; nonlinear control; switched system
