arXiv subjects

Gia Quoc Bao Tran

Publications and source records attributed to Gia Quoc Bao Tran.

3 recordsLinked to original sources

arXiv2026

Interval Observer Design Using Observability Decomposition for Detectable Linear Systems

We provide a systematic interval observer design method for detectable linear time-invariant (LTI) systems, where a part of the state is observable from the measured output. An observability-based invertible LTI transformation decomposes the state into two parts. The first part is decoupled from the other and observable from the output, while the second is affected by the first, does not appear in the output, but is detectable. A Sylvester-based LTI interval observer is designed for the first part. For the second part, a Jordan-based linear time-varying interval observer is built, treating the interaction from the first part as inputs with known bounds. The intervals in the original coordinates are constructed either by inverting the decomposition online for the intervals in the transformed coordinates or by directly implementing the observer written in the original coordinates. Academic examples illustrate the interest of our approach.

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arXiv2025

Systematic interval observer design for linear systems

We first develop systematic and comprehensive interval observer designs for linear time-invariant (LTI) systems, under standard assumptions of observability and interval bounds on the initial condition and uncertainties. Traditionally, such designs rely on specific transformations into Metzler (in continuous time) or non-negative (in discrete time) forms, which may impose limitations. We demonstrate that these can be effectively replaced by an LTI transformation that is straightforward to compute offline. Subsequently, we extend the framework to time-varying systems, overcoming the limitations of conventional approaches that offer no guarantees. Our method utilizes dynamic transformations into higher-dimensional target systems, for which interval observers can always be constructed. These transformations become left-invertible after a finite time, provided the system is observable and the target dynamics are sufficiently high-dimensional and fast, thereby enabling the finite-time recovery of interval bounds in the original coordinates. Academic examples are provided to illustrate the proposed methodology.

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arXiv2024

A Unified KKL-based Interval Observer for Nonlinear Discrete-time Systems

This work proposes an interval observer design for nonlinear discrete-time systems based on the Kazantzis-Kravaris/Luenberger (KKL) paradigm. Our design extends to generic nonlinear systems without any assumption on the structure of its dynamics and output maps. Relying on a transformation putting the system into a target form where an interval observer can be directly designed, we then propose a method to reconstruct the bounds in the original coordinates using the bounds in the target coordinates, thanks to the Lipschitz injectivity of this transformation achieved under Lipschitz distinguishability when the target dynamics have a high enough dimension and are pushed sufficiently fast. An academic example serves to illustrate our methods.

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