Interval Observers Design for Non-Stationary Systems

The paper is devoted to the problem of interval observers design for technical systems described by non-stationary linear dynamic equations under unmatched disturbances and measurement noise. The problem is to design the observer with fewer dimensions than that of the original system; such an observer must generate upper and lower bounds of admissible values of the prescribed linear function of the original system state vector. To construct the interval observer, the reduced-order model of the original system insensitive to the disturbances is designed. It is assumed that the reduced-order model is realized in the diagonal Jordan canonical form. The main advantage of such a form is that it has the main properties which are necessary to the interval observer design and to take into account non-stationarity of the system. As a result, the model is stationary and nonlinear. Besides, such a model allows to reduce limitations on the system under which the interval observer can be designed. The interval observer consists of two subsystems: the first one generates the lower bound, the second one the upper bound. The relations describing both subsystems are given. To take into account the nonlinearities, the notion of monotony of the output variables entering in the nonlinear term on the model is introduced. This notion allows finding out how the upper and lower bounds of these variables will appear in the interval observer. To reduce the interval width, the sliding mode observer is suggested to use. Such an observer is intended to estimate the value of the external disturbances; this estimate is used then in the interval observer to compensate the disturbances. Theoretical results are illustrated by practical example of the electric servoactuator for which the interval observer is designed.