A general class of linear time invariant systems with delay is studied. Recently, they attracted considerable interest in the and control community. The complexity arises due to exponential type transcendental terms their characteristic equation. transcendentality brings infinitely many roots, which are cumbersome elaborate as evident from literature. number methodologies have been suggested limited ability assess stability parametric domain delay. This study offers an exact, structured...

Time-delays are important components of many dynamical systems that describe coupling or interconnection between dynamics, propagation, transport phenomena in shared environments, heredity, and competition population dynamics. This monograph addresses the problem stability analysis stabilisation subjected to time-delays. It presents a wide self-contained panorama analytical methods computational algorithms using unified eigenvalue-based approach illustrated by examples applications...

Stability analysis of a single-lane microscopic car-following model is studied analytically from the perspective delayed reactions human drivers. In literature, drivers are modeled with discrete delays, which assume that make their control decisions based on stimuli they receive point time in history. We improve this by introducing distribution assumes actions information distributed over an interval Such assumption more realistic, as it takes into consideration memory capabilities and...

An intriguing perspective is presented in studying the stability robustness of systems with multiple independent and uncertain delays. It based on a holographic mapping, which implemented over domain This mapping considerably alleviates problem, otherwise known to be notoriously complex. creates dramatic reduction dimension problem from infinity manageably small number. Ultimately process reduced within finite dimensional cube edges length 2pi new domain, what we call building block. In...

This note presents a design technique for the delay-based controller called proportional integral retarded (PIR), which solves regulation problem of general class stable second-order LTI systems. Using spectral analysis, yields tuning strategy PIR by placing triple real dominant root closed-loop system. result ultimately guarantees desired exponential decay rate σ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> while achieving as an...

Delay-independent stability (DIS) of a general class linear time-invariant (LTI) multiple time-delay system (MTDS) is investigated in the entire delay-parameter space. Stability such systems may be lost only if their spectrum lies on imaginary axis for some delays. We build an analytical approach that requires inspection roots finite number single-variable polynomials order to detect ever delays, excluding infinite The enables test necessary and sufficient conditions DIS LTI-MTDS,...

The occurrence of the regenerative chatter phenomenon in milling process is studied for cutters with non-uniform distribution (called variable-pitch cutters). dynamic model developed and evaluated from stability point view. mathematical characterization problem falls within a general class delay differential equations (DDE) multiple rationally independent delays. contribution this paper adoption mathematically novel very recent paradigm to determine analytically bounds stable versus unstable...

A consensus-control protocol is designed and implemented here on a three-robot system arranged horizontal platform, in which camera used to track robot positions, personal computer broadcasts commands the robots based this via Bluetooth connection, where such are affected by time delays. The design involves some salient features of graph-based approach, an input-output linearization scheme, addressing uncertainties control problem. By implementing experiments, we show that consensus can be...

This paper explores the deliberate introduction of delays in feedback loops and their positive impact on linear time-invariant, single-input, single-output (LTI-SISO) systems. The delay, considered as a design parameter, is intentionally induced using class delay-based controllers, aiming at improving closed-loop system performance by deploying pole-placement technique to attain fastest velocity response control commands. technique, based an algebraic geometric analysis, able extract exact...

This article considers the containment of heterogeneous linear time-invariant multi-human multi-agent systems with a distributed dynamic state feedback control law. The unique aspect this problem lies in presence multiple human operators. Each operator commands subset agents while observing same or different subset. Commanding based on their observation approach operators makes them integral components network rather than simple providers reference signals. setup requires new set conditions...

A new methodology, advanced clustering with frequency sweeping (ACFS), is introduced for the stability analysis of most general class linear time-invariant time-delay systems multiple delays. ACFS a cross fertilization algebraic geometry, technique and root paradigm, it can directly extract 2-D sections views in any two-delay domain. In this domain, also test delay-independent based on necessary sufficient conditions, compute, delay-dependent case, precise lower upper bounds only parameter,...

We investigate the use of a derivative-free control scheme called multiple-delay proportional-retarded (PR) protocol to achieve fast consensus in large-scale multiagent system. The delays are intentionally introduced PR with purpose creating derivative-like controllers that rely only on position measurements, thus mitigating undesirable noise effects. main result places spectral abscissa dynamics at desired locus and also achieves user-defined "separation," both which directly influence...

A novel analytical tool is presented to assess the stability of simultaneous machining (SM) dynamics, which also known as parallel machining. In SM, multiple cutting tools, are driven by spindles at different speeds, operate on same workpiece. Its superior efficiency main reason for using SM compared with traditional single (STM). When optimized in sense maximizing rate metal removal constrained machined surface quality, typical “chatter instability” phenomenon appears. Chatter instability...

A trajectory-tracking problem is considered for a linear time invariant (LTI) dynamics with fixed control law. However, the feedback line affected by multiple delays. The stability of becomes complex problem. It well known that time-delayed LTI systems may exhibit stable operating zones (which we call pockets) in space Our aim this paper to locate and experimentally validate these pockets. For analytical determination pockets utilize new methodology, cluster treatment characteristic roots...

This study investigates the stability of a class single-delay interconnected dynamics where share only delayed information with each other while seeking consensus in large scale network fixed topology. The coupled dynamics, which are infinite dimensional because presence delays, can remain stable for at most certain amount delays called delay margin. margin is intricately determined by nature connectivity and coupling strengths among dynamics. Here we present systematic approach to correlate...