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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.

The problem of output stabilization of a class of nonlinear systems subject to parametric and signal uncertainties is studied. 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 (LPV) systems without assumption that the vector of scheduling parameters is available for measurements. Efficiency of the proposed approach is demonstrated through two examples.

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International audienceInterval state observers provide an estimate on the set of admissible values of the state vector at each instant of time. Ideally, the size of the evaluated set is proportional to the model uncertainty, thus interval observers generate the state estimates with estimation error bounds, similarly to Kalman filters, but in the deterministic framework. Main tools and techniques for design of interval observers are reviewed in this tutorial for continuous-time, discrete-time and time-delayed systems

In this paper, the problem of design of interval observers for Linear-Parameter-Varying (LPV) systems, containing non detectable or non strongly observable parts, is addressed. Firstly, a High Order Sliding Mode (HOSM) method is applied to the strongly observable subsystem, obtained by an appropriate change of coordinates, to estimate the state and its derivative. Secondly, this information is used to decrease the level of uncertainty in the rest of the system, which leads to improvement of accuracy of the set-membership estimates generated by an interval observer. Moreover, it is shown that HOSM techniques allows us to relax the applicability conditions of standard interval observer design methods. The efficiency of the proposed approach is demonstrated through simulation examples.

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An approach to interval observer design for Linear Parameter-Varying (LPV) systems is proposed. It is assumed that the vector of scheduling parameters in LPV models is not available for measurement. Two different interval observers are constructed for nonnegative systems and for a generic case. Stability conditions are expressed in terms of matrix inequalities, which can be solved with respect to the observer gains using standard numerical solvers. Applying L1/L2 framework the robustness and estimation accuracy with respect to model uncertainty are analyzed. The efficiency of interval estimation for LPV models is demonstrated through numerical experiments for a microfluidic system and an academic example. I. INTRODUCTIONState estimation is an important issue in many engineering fields [1], [2], [3]. Estimated states may be required, for example, for control design or fault detection. This problem has been widely studied in the literature and many solutions already exist for linear systems and a number of nonlinear structures. For the latter situation, the observer design problem is solvable if the system model can be transformed into a canonical form, which may be a hard assumption to satisfy in many applications. To solve the problem, an appealing approach is based on the LPV transformation of the nonlinear system [4], [5], [6], [7].Note that Takagi-Sugeno decomposition can be another alternative solution to deal with nonlinear systems and to obtain the equivalent representation by a compact set of linear state space models with nonlinear weighting functions satisfying the convex sum property [8], [9]. In the presence of uncertainty (unknown parameters or/and external disturbances) the design of a conventional estimator, converging to the ideal value of the state, cannot be realized. However, an interval estimation may still remain feasible: an observer can be constructed that, using input-output information, evaluates the set of admissible values (interval) for the state at each instant of time. The interval length has to be minimized and it is proportional to the size of the model uncertainty. Despite such a formulation looks like a simplification of the state estimation problem, in fact it is an improvement since the interval mean can be used as the state pointwise estimate, while the interval limits give the admissible deviations from that value (thus, an interval estimator provides a simultaneous accuracy evaluation for bounded uncertainty, which may not have a known statistics). There are several approaches to design interval/set-membership estimators [10], [11], [12], [13]. This paper continues the trend of interval observer design based on the monotone systems theory [12], [13], [14], [15], [16]. In such a way the main restriction for the interval observer design consists in providing cooperativity of the interval estimation error dynamics by a proper design. Such a complexity has been recently overcame in [17], [15], [18] for LTI systems. In those studies, it has beenshown that under some mild condition...