Section: New Results

Interval control and estimation

Participants : Denis Efimov, Wilfrid Perruquetti.

In many cases due to parametric and/or signal uncertainties presented in a plant model it is not possible to design a conventional observer, which provides a point-wise estimate of state in a finite time or asymptotically. In this case it is still frequently possible to apply the interval observer techniques, which generate an estimate on the interval of the admissible values of the state at the current instant of time. The recent results are listed below:

• The problem of output stabilization of a class of nonlinear systems subject to parametric and signal uncertainties is studied in [20] , [21] . First, an interval observer is designed estimating the set of admissible values for the state. Next, it is proposed to design a control algorithm for the interval observer providing convergence of interval variables to zero, that implies a similar convergence of the state for the original nonlinear system. An application of the proposed technique shows that a robust stabilization can be performed for linear time-varying and linear-parameter-varying systems without assumption that the vector of scheduling parameters is available for measurements.

• The problem of interval observer design for a class of observable nonlinear systems is studied in [33] . It is shown that under some mild conditions a Hurwitz matrix can be transformed to a Hurwitz and Metzler one using a real similarity transformation.

• The work [64] is devoted to interval observer design for Linear Time Varying (LTV) systems and a class of nonlinear time-varying systems in the output canonical form. An interval observer design is feasible if it is possible to calculate the observer gains making the estimation error dynamics cooperative and stable. It has been shown that under some mild conditions the cooperativity of an LTV system can be ensured by a static linear transformation of coordinates. The case of a time-varying transformation for periodic systems is considered in the work [64] .

• The problem of actuator fault detection for flat systems using the sliding-mode differentiation and the interval constraint satisfaction technique has been analysed in [43] .