Interval state observer for nonlinear time varying systems

Abstract

This paper is devoted to design of interval observers 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 is shown that under some mild conditions the cooperativity of an LTV system can be ensured by a static linear transformation of coordinates. The efficiency of the proposed approach is demonstrated through numerical simulations.

On set-membership observer design for a class of periodical time-varying systems

“…In the work [7] such a restriction has been avoided. First, to introduce that result we need the following assumptions.…”

“…In order to apply the approach of interval observer design to the systems with non-constant matrices dependent on measurable input-output signals and time, an extension of the result from [21] has been presented in [7], which allows one to calculate a constant similarity transformation matrix representing a given interval of matrices to an interval of Metzler matrices (this result is introduced in Section 3 for completeness and comparison). This method can be used to design interval observers for Linear-Parameter-Varying (LPV) systems [17], [23], [25] with measurable vector of scheduling parameters.…”

Comparison of set-membership and interval observer approaches for state estimation of uncertain systems

“…In stochastic approaches, noises and perturbations are assumed to be described by some known statistical distribution (typically Gaussian) but deterministic approaches consider noises and disturbances as unknown variables with known bounds. Inside the family of deterministic approaches, the interval state observers and set-membership state estimators have been introduced separately [2], [3], [4]. The state estimation provided by both approaches is given in a form of a set of states at each time instant.…”

Interval observer design for Linear Parameter-Varying systems subject to component faults

“…For instance, in [4] an interval observer design for discrete-time LPV systems has been developed assuming that the vector of scheduling parameters is not available for measurement. The case of known scheduling vector has been proposed in [6] using a static transformation of coordinates.…”