Simple interval observers for linear impulsive systems with applications to sampled-data and switched systems
This work provides a systematic method for interval observer design in hybrid systems, which is relevant for control engineers dealing with sampled-data and switched systems.
The paper develops sufficient conditions for designing simple interval observers for linear impulsive systems with minimum and range dwell-time constraints, formulated as infinite-dimensional linear programs. The approach is constructive, allowing observer gain extraction, and is validated on three examples including impulsive, sampled-data, and switched systems.
Sufficient conditions for the design of a simple class of interval observers for linear impulsive systems subject to minimum and range dwell-time constraints are obtained and formulated in terms of infinite-dimensional linear programs. The proposed approach is fully constructive in the sense that suitable observer gains can be extracted from the solution of the optimization problems and is flexible enough to be extended to include performance constraints and parametric uncertainties. In order to be solvable, the infinite-dimensional linear programs are relaxed using a method based on sum of squares which is known to be asymptotically exact in the present case. Three examples are given for illustration: the first one pertains on the interval observation of an impulsive system under a minimum dwell-time constraint, the second one is about the interval observation of an aperiodic sampled-data system and the last one is about the interval observation of a linear switched system.