LMI‐based reset unknown input observer for state estimation of linear uncertain systems

Abstract

This paper proposes a novel kind of Unknown Input Observer (UIO) called Reset Unknown Input Observer (R-UIO) for state estimation of linear systems in the presence of disturbance using Linear Matrix Inequality (LMI) techniques. In R-UIO, the states of the observer are reset to the after-reset value based on an appropriate reset law in order to decrease the L 2 norm and settling time of estimation error. It is shown that the application of the reset theory to the UIOs in the LTI framework can significantly improve the transient response of the observer. Moreover, the devised approach can be applied to both SISO and MIMO systems. Furthermore, the stability and convergence analysis of the devised R-UIO is addressed. Finally, the efficiency of the proposed method is demonstrated by simulation results.

Optimal reset unknown input observer design for fault and state estimation in a class of nonlinear uncertain systems

“…Considering the effect of temporal regularization, if the R-UIO hits the reset sector and τ ≤ ρ, it has to continue flowing until τ > ρ. In this case stability cannot be assured [40]. To deal with this problem, for a very small ρ a slightly inflated flow region can be considered [38].…”

“…In [39], the application of reset strategy to a proportional-integral observer for fault estimation problem is investigated. In [40] reset unknown input observer for linear systems is designed. In [41] reset proportional-integral observer for time-varying dynamics is developed.…”

A sufficient condition to design unknown input observers for nonlinear systems with arbitrary relative degree

“…Remark 4. Notice that the estimation dynamics in (7) depends on the matrix valued function Q(x), which can be determined only if x ∈ 𝒟 , as one can see from (6) and Assumption 1. Thus, it is required to constrain the trajectories of x on 𝒟 to ensure the rank condition and the correct operation of the nonlinear UIO.…”

“…Note that the matrix Γ(x) is nonsingular for all x ∈ R 2 and rank(Γ(x)) = rank(g(x)) = 1, ∀x ∈ R 2 . The matrix Q(x) is thus obtained by solving (6), which admits the solution…”

Robust Polytopic-LPV Body-Weight-Dependent Control of Blood Glucose in Type-1 Diabetes

“…During the last decades, polytopic-LPV techniques have received a great deal of attention due to their practical applications in a wide range of areas. Mostly, the whole system states are not measurable to be involved in the feedback, and also, some measuring errors of system parameters appear because of sensor errors and imprecision [26]- [28]. In such cases, the output data is utilized for feedback instead of state vector data.…”