Input Redundancy of Switched Linear Systems via Polynomial Parameter-Dependent Systems

In this letter, we introduce a definition of input redundancy for switched systems, particularly focusing on the continuous input. We establish a criterion for assessing whether a switched linear system is input redundant with respect to the continuous input. Our approach initially involves transforming the switched linear system into a linear system depending polynomially on a univariate parameter through Lagrange polynomial interpolation. This allows us to leverage recent results in geometric control theory and input redundancy for parameter-dependent systems, and adapt them to the context of switched systems in order to obtain the desired conditions. To illustrate the application of the proposed strategy, we provide two numerical examples.