Robustness Against Matched Uncertainty by Linear State-Feedback Controller Combined with Internal Saturation

This note shows robustness against so-called “matched uncertainty” of Linear Parameter-Varying (LPV) systems can be ensured by linear state-feedback controllers combined with internal saturation. It is well-known that Sliding Mode Control (SMC) has strong robustness against matched uncertainties, i.e. the uncertainties belonging to the image of the control input matrix. This property makes SMC useful in many practical application fields, e.g. Fault-Tolerant Control (FTC), Fault Detection and Identification (FDI), etc. However, this property is not unique to SMC, and this note shows that it also holds for a control scheme based on linear state-feedback controllers combined with internal saturation. For the implementation of SMC, modified signum functions, i.e. sigmoid-like functions with smoothing factors, are often used instead of ideal ones to avoid chattering. This note clarifies that the role of the smoothing factors in diagonalization SMC is characterized as the reciprocal of the gains for switching functions, and proves that linear state-feedback controllers combined with internal saturation have smaller boundary layers than diagonalization SMC with sigmoid-like functions.