2024/05/10 by Thach Ngoc Dinh, Dinh, Thach Ngoc, Gia Quoc Bao Tran +1
Computer Science · Engineering · #Advanced Control Systems Optimization #Control Systems and Identification #FOS: Electrical engineering #Numerical Methods and Algorithms #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2405.06445
openalex publication_date 2024/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.