Immersion of a class of nonlinear systems into state‐affine ones for the design of generalized parameter estimation‐based observers: A simple algebraic procedure

Generalized parameter estimation‐based observers have proven very successful in dealing with systems described in state‐affine form. In this paper, we enlarge the domain of applicability of this method, proposing an algebraic procedure to immerse an ‐dimensional general nonlinear system into an ‐dimensional system in state‐affine form, with . It is well‐known that the necessary and sufficient condition for the solution of the general immersion problem requires the solution of a partial differential equation that, moreover, has to satisfy a restrictive injectivity condition. Given the complexity of this task, we propose an alternative simple algebraic method to identify the required dynamic extension and coordinate transformation, a procedure that, as shown in the paper, is rather natural for physical systems. We illustrate the method with some academic benchmark examples from observer theory literature—that, in spite of their apparent simplicity, are difficult to solve with the existing methods—as well as several practically relevant physical examples.