Measurable Disturbance Rejection with Quadratic Stability in Continuous-Time Linear Switching Systems

It is well-known that disturbances with different features (i.e., inaccessible, measurable, or previewed disturbances) must be handled with the appropriate compensation schemes: namely, those which better exploit the available information. In particular, this work is focused on rejection of disturbances accessible for measurement in continuous-time linear switching systems, with the requirement that the compensated system be quadratically stable under arbitrary switching. A dynamic feedforward switching compensator is designed on the assumption that the plant be quadratically stable under arbitrary switching. This assumption can be relaxed to quadratic stabilizability by linear state feedback and by linear output injection, provided that a measurement dynamic feedback stabilizer is also devised. The proposed techniques apply to linear switching systems whose modes may be either left-invertible or not. The methodology adopted is based on the use of the geometric approach enhanced with stability notions which are typically considered in linear switching systems.