arXiv subjects

Hieu Trinh

Publications and source records attributed to Hieu Trinh.

12 recordsLinked to original sources

arXiv2026

Observer-Based Target Control for Mismatched Time-Delay Systems

This paper addresses observer-based target control for linear time-delay systems subject to simultaneous, mismatched input and output latencies. While full-state regulation is often conservative and computationally intensive, practical engineering objectives typically require controlling only specific linear combinations of states, or target outputs. To overcome the challenges posed by these asymmetric, dual-channel delays, we propose a reduced-order modeling framework inspired by the structural philosophy of Fernando and Darouach \cite{Fernando2025}. By projecting the high-dimensional plant dynamics onto the row space of the target output matrix $F_o$, the controller focuses strictly on the lower-dimensional target subspace. Based on this projection, an observer-based control scheme is developed to ensure precise target stabilization despite the simultaneous, mismatched input, state, and output latencies.

eess.SY↗

arXiv2026

Delayed Functional Observers for the Realization of Generalized Delayed Control Laws

Building on the collective advancements in the literature \cite{trinh1, trinh2, trinhnn26, trinhnam26, trinhnam1}, this paper proposes the design of delayed functional observers to asymptotically estimate a generalized delayed control law under significant input and output delays. This framework enables designers to extend the allowable bounds for input delays while ensuring that the observer-based control scheme stabilizes the system despite simultaneous mismatched input and output time-delays.

eess.SY↗

arXiv2026

On Time-Delay Compensators for Delayed-Output Systems

This paper advances the practical utility of functional observer theory by addressing sensing latency in linear time-delay systems. We address the estimation of the functional $z(t)=Fx(t)$ in cases where the measurement delay $h$ is independent of the internal state delay $\tau$, with a specific focus on the condition $0 < h < \tau$. To compensate for sensing lags, we propose a functional observer structure characterized by multiple internal delays and an augmented architecture. Algebraic existence conditions are established alongside a constructive synthesis procedure. By incorporating an additional delayed measurement vector, we demonstrate that this approach significantly expands the design space and is applicable to a wider class of systems with larger state and output delays.

eess.SY↗

arXiv2026

Delayed Functional Observers for Output-Delayed Linear Systems

This paper introduces a novel class of delayed functional observers specifically designed to reconstruct delayed control laws under severe output measurement lags, directly complementing recent literature \cite{trinhnn26, trinhnam26}. By systematically mitigating simultaneous, unequal delays across both the actuator and sensor channels, the proposed architecture resolves dual-channel latency without requiring full-state estimation or computationally intensive real-time distributed integration. Ultimately, this work provides a powerful, low-order framework that bridges the gap between idealized control theory and the practical constraints of modern networked engineering systems.

eess.SY↗

arXiv2026

Observer-Based Control of Linear Systems with Mismatched Input and Output Delays

This paper investigates the stabilization of linear systems subject to simultaneous, mismatched time delays in both the control input and system output vectors. The proposed control framework is developed in two primary stages. First, an asymptotically stabilizing delayed state-feedback controller is synthesized by leveraging recent advancements in Linear Matrix Inequality (LMI) techniques. Second, this controller is realized using novel time-delay compensators \cite{trinhnam26}. This architecture successfully accommodates an output measurement delay $\tau_y$ that is independent of the input delay $\tau_u$, enabling direct estimation of the delayed state-feedback control law. The proposed methodology is then extended to target output controllers to account for simultaneous, mismatched time delays in both the control input and system output vectors.

eess.SY↗

arXiv2026

Existence and Design of Functional Observers for Time-Delay Systems with Delayed Output Measurements

This paper investigates the problem of functional state estimation for linear time-delay systems in which the delay affecting the state evolution differs from the delay affecting the output measurements. While existing observer designs typically assume instantaneous output availability, practical systems often exhibit measurement delays that are distinct from and not aligned with the intrinsic state delay. We explicitly distinguish between the state delay $\tau$ and the measurement delay $h$ and address the problem of estimating a desired functional $z(t)=Fx(t)$ under such mismatched delay conditions. Three functional observer structures are proposed to accommodate different delay configurations, each capable of realizing functional observers of different orders. This flexibility is important since a functional observer whose order equals the number of estimated functionals may not always exist. For each structure, algebraic existence conditions are established together with constructive synthesis procedures. A functional augmentation framework is developed to derive verifiable rank-based conditions for observers of various orders. In addition, the notion of generalized functionals, defined over an augmented delayed state vector, is introduced to provide greater flexibility in satisfying observer existence conditions and facilitating systematic design. Numerical examples illustrate the proposed theory.

eess.SY↗

arXiv2025

Observer-based Differentiators for Noisy Signals

We present a collection of different types of observation systems that work as differentiators. These observer-based differentiators can produce estimates for derivatives of a given signal, even though the given signal is prone to noise.

eess.SY↗

arXiv2021

Learning to Emphasize: Dataset and Shared Task Models for Selecting Emphasis in Presentation Slides

Presentation slides have become a common addition to the teaching material. Emphasizing strong leading words in presentation slides can allow the audience to direct the eye to certain focal points instead of reading the entire slide, retaining the attention to the speaker during the presentation. Despite a large volume of studies on automatic slide generation, few studies have addressed the automation of design assistance during the creation process. Motivated by this demand, we study the problem of Emphasis Selection (ES) in presentation slides, i.e., choosing candidates for emphasis, by introducing a new dataset containing presentation slides with a wide variety of topics, each is annotated with emphasis words in a crowdsourced setting. We evaluate a range of state-of-the-art models on this novel dataset by organizing a shared task and inviting multiple researchers to model emphasis in this new domain. We present the main findings and compare the results of these models, and by examining the challenges of the dataset, we provide different analysis components.

cs.CL↗

arXiv2018

On asymptotic properties of solutions to fractional differential equations

We present some distinct asymptotic properties of solutions to Caputo fractional differential equations (FDEs). First, we show that the non-trivial solutions to a FDE can not converge to the fixed points faster than $t^{-α}$, where $α$ is the order of the FDE. Then, we introduce the notion of Mittag-Leffler stability which is suitable for systems of fractional-order. Next, we use this notion to describe the asymptotical behavior of solutions to FDEs by two approaches: Lyapunov's first method and Lyapunov's second method. Finally, we give a discussion on the relation between Lipschitz condition, stability and speed of decay, separation of trajectories to scalar FDEs.

math.CA↗

arXiv2018

Stability of fractional-order nonlinear systems by Lyapunov direct method

In this paper, by using a characterization of functions having fractional derivative, we propose a rigorous fractional Lyapunov function candidate method to analyze stability of fractional-order nonlinear systems. First, we prove an inequality concerning the fractional derivatives of convex Lyapunov functions without the assumption on the existence of derivative of pseudo-states. Second, we establish fractional Lyapunov functions to fractional-order systems without the assumption on the global existence of solutions. Our theorems fill the gaps and strengthen results in some existing papers.

math.CA↗

arXiv2017

A linearized stability theorem for nonlinear delay fractional differential equations

In this paper, we prove a theorem of linearized asymptotic stability for fractional differential equations with a time delay. More precisely, using the method of linearization of a nonlinear equation along an orbit (Lyapunov's first method), we show that an equilibrium of a nonlinear Caputo fractional differential equation with a time delay is asymptotically stable if its linearization at the equilibrium is asymptotically stable. Our approach based on a technique which converts the linear part of the equation into a diagonal one. Then using properties of generalized Mittag-Leffler functions, the construction of an associated Lyapunov--Perron operator and the Banach contraction mapping theorem, we obtain the desired result.

math.CA↗

arXiv2015

New summation inequalities and their applications to discrete-time delay systems

This paper provides new summation inequalities in both single and double forms to be used in stability analysis of discrete-time systems with time-varying delays. The potential capability of the newly derived inequalities is demonstrated by establishing less conservative stability conditions for a class of linear discrete-time systems with an interval time-varying delay in the framework of linear matrix inequalities. The effectiveness and least conservativeness of the derived stability conditions are shown by academic and practical examples.

math.OC↗