A simple finite-time distributed observer design for linear time-invariant systems

Abstract

A design of a distributed observer is proposed for continuous-time systems with nonlinear observer nodes such that the estimation errors converge in a finite time to zero. By taking advantage of individual observability decompositions, the designs for the locally observable and the unobservable substate are made independent from each other. For the observable substate of each node, standard centralized finite-time observer techniques are applied. To estimate distributively the unobservable substate, the observer nodes employ consensus coupling in a linear term and an additional term embedded in a fractional power. The approach is derived using homogeneity arguments and it leads to a simple design with an LMI that is guaranteed to be feasible under general conditions.

Distributed Observers for LTI Systems with Finite Convergence Time: A Parameter Estimation-based Approach

“…Although it is possible to add this feature to the independent state estimators proposed here, we avoid this solution and concentrate, instead, in the reconstruction of the full state via direct information exchange between the nodes. Luenberger observer-based DSEs that enjoy the FCT property have already been reported in [18], [19], [20]. Our GPEBO-based DSE outperforms these designs due to the following considerations.…”

Fixed-Time Stabilization of Linear Delay Systems by Smooth Periodic Delayed Feedback

“…The periodic gain K (Ac,h) (t) in (39) depends on the closed-loop system matrix Ac. We next establish a method where only the openloop system matrix A is involved.…”

“…where K0 and K (Ac,h) (t) are the same as that in (40) and (39), and h > 0 is some constant. The initial condition z(s), s ≤ 0 can be arbitrarily chosen.…”

“…Problems of this nature are relevant to such tasks as precision tracking and localization, and are reminiscent of the traditional deadbeat or "ripple-free" control (see, e.g., [13], [14]). By now several efficient methods have been developed for achieving finite-time stabilization, including those by sliding mode control [37], by a Lyapunov differential inequality-based approach [4], [42], that by a homogeneous approach [5], [11], [17] (see also [38], [39] for its use to design distributed finite-time observers), and by an implicit Lyapunov function approach [35]. It is worth noting that in these methods the convergence time generally depends on and hence varies with the initial condition.…”

On finite-time stability analysis of homogeneous Persidskii systems using LMIs

“…However, in general case, these LMIs are infeasible for homogeneous Persidskii systems due to homogeneity imposes some restrictions on system matrices (e.g., linear part of the system is presented or can be reduced to the form A 0 x, x ∈ R n with a nilpotent matrix A 0 ∈ R n×n ), and the approach of [17] does not take into account a possible homogeneity of the system, then the used Lyapunov function cannot be homogeneous. In some cases this problem can be handled with the use of homogeneous approximations as in [25]. However, this approach does not allow to obtain settling time estimations and does not provide quantitative robustness analysis.…”