Robust Sampled-Observer-Based Switching Law for Uncertain Switched Affine Systems Subject to Sensor Faults With an Application to a Bidirectional Buck-Boost DC-DC Converter

This paper proposes a robust sampled-observer-based fault-tolerant min-type switching law for a class of continuous-time uncertain switched affine systems (SAS) subject to persistent bounded sensor faults using Luenberger observers to estimate the system state. The switching law is designed to make the trajectories of the system be attracted to an open ball containing a given equilibrium point, even in the presence of faults and norm-bounded uncertainties. First, nonlinear matrix conditions are given to obtain the switching law that guarantee the practical stability of a class of uncertain SAS whenever persistent bounded sensor faults are present. To reduce the complexity of the nonlinear matrix conditions, we thus provide LMI-based conditions to obtain the observer gains at the cost of increasing the estimation of the ball for which the trajectories of the system are attracted. Next, we estimate the radius of the open ball by solving a minimization problem using the gains obtained by satisfying the LMI conditions. We then propose an algorithm to search for a set of equilibrium points for a class of uncertain SAS with two system modes, which can be applied to DC-DC converters such as boost, buck, buck-boost, and Cuk converters. Finally, experiments using hardware in the loop of a bidirectional buck-boost DC-DC converter illustrate the efficiency of the fault-tolerant strategy.