Stability analysis for time-delay systems with partial states subject to impulsive inputs

This paper studies stability analysis of linear time-invariant time-delay feedback systems consisting of a finite-dimensional system and a pure delay. The continuous-time state transition is described by the monodromy operator in discrete-time through the lifting technique, and a stability condition in terms of its spectral radius is first restated in terms of the norm of a power of the operator. Quasi-finite-rank approximation is then applied on the power of the operator, and by evaluating the effect of the approximation error on the norm, a new necessary and sufficient stability condition is given finally.

ABSTRACTThis paper investigates the problem of exponential stability analysis of linear time-delay systems. First, based on the Gram-Schmidt-based integral inequality and the Taylor expansion of exponential function, we develop a new weighted multiple integral inequality called Taylor expansion-based weighted integral inequality. Second, a new Lyapunov-krasovskii functional is constructed, and then, with the help of the Taylor expansion-based inequality, a new exponential stability criterion is established in terms of linear matrix inequality. Finally, numerical examples are presented to show the effectiveness of the newly established stability criterion.

This paper studies the consensus problem of first-order and second-order multi-agent systems with nonlinear dynamics and quantised interactions. Continuous-time and impulsive control inputs are designed for the multi-agent systems on the logarithmic quantised relative state measurements of agents, respectively. By using nonsmooth analysis tools, we get some sufficient conditions for the consensus of multi-agent systems under the continuous-time inputs. Compared with continuous-time control inputs, impulsive distributed control inputs just use the state variables of the systems at discrete-time instances. Based on impulsive control theory, we prove that the multi-agent systems can reach consensus by choosing proper control gains and impulsive intervals. The simulation results are given to verify the effectiveness of the theoretical results.

The method of Implicit Lyapunov-Krasovski Functional (ILKF) for stability analysis of time-delay systems is introduced. Theorems on Lyapunov, asymptotic, (hyper) exponential, finite-time and fixed-time stability analysis using ILKF are presented. The hyper exponential stabilization algorithm for a time-delay system is presented. The theoretical result is supported by numerical simulation.

Some sufficient conditions for exponential stability of linear neutral functional differential equations

Improved stability criterion and output feedback control for discrete time-delay systems

A new multiple integral inequality and its application to stability analysis of time-delay systems

This paper investigates the stability analysis and stabilization problems for a class of nonlinear time-delay systems described by conformable derivatives. We consider systems with one-sided Lipschitz nonlinearities and quadratic inner-boundedness conditions, which encompass a broad range of practical applications. Through the construction of appropriate Lyapunov-Krasovskii functionals, we develop novel linear matrix inequality (LMI) conditions for exponential stability of autonomous systems and practical exponential stability for systems subject to bounded perturbations. Furthermore, we propose state-feedback stabilization strategies that transform the controller design problem into a convex optimization framework solvable via efficient LMI techniques. The theoretical developments are comprehensively validated through numerical examples that demonstrate the effectiveness of the proposed stability and stabilization criteria. The results establish a rigorous framework for analyzing and controlling conformable fractional-order systems with time delays, bridging theoretical advances with practical implementation considerations.

Planar juggling of a devil-stick using impulsive inputs is addressed using the concept of discrete virtual holonomic constraints (DVHC). The location of the center-of-mass of the devil-stick is specified in terms of its orientation at the discrete instants when impulsive control inputs are applied. The discrete zero dynamics (DZD) resulting from the choice of DVHC provides conditions for stable juggling. A control design that enforces the DVHC and an orbit stabilizing controller are presented. The approach is validated in simulation.

Improved delay-dependent stability criteria for neutral systems with mixed interval time-varying delays and nonlinear disturbances

The stability analysis of time-delay systems is a tough task even in the linear case, especially when time-varying delays are considered. In recent years, for the class of positive delay systems, a number of insightful works appeared in the literature, highlighting their peculiar stability properties, which lead to simple and easy to check necessary and sufficient conditions for the delay-independent stability. This fact poses the question whether some results that hold for positive systems can be exported to arbitrary systems. In some recent papers we gave an answer to this question by extending to the time-delay setting the Internally Positive Representation technique, a method that allows to systematically construct positive representations of arbitrary systems. In this work, after a survey on recent stability results for positive delay systems, an overview of the Internally Positive Representation technique and of its implications on the stability analysis of arbitrary systems is reported. Three classes of linear systems are considered: delay differential, delay difference, and coupled delay differential-difference systems.

A new quasi-finite-rank approximation of compression operators on [formula omitted] with applications to sampled-data and time-delay systems: Piecewise linear kernel approximation approach

A generalized proportional Caputo fractional model of multi-agent linear dynamic systems via impulsive control protocol

New model transformations for the stability analysis of time-delay systems

The use of active vibration control may induce a delay leading to detrimental degradation of the performance of active vibration control. This is particularly true in the case of mechanical systems subjected to friction-induced vibration and noise for which such time-delays can lead to the appearance of undesirable instability. Furthermore, conducting a stability analysis of time-delay systems and estimation of the critical time delay are challenging, due to the infinite nature of the characteristic (quasi) polynomial of the associated closed-loop system, having an infinite number of roots.The objective of this paper is to discuss a strategy for the estimation of the critical time delay for the problem of Friction-Induced Vibration and noisE (FIVE). To achieve such an objective, the prediction of the stability analysis of time delay systems and the estimation of the associated critical time delay are first performed by applying the frequency sweep test and the eigenvalue problem approximation using the Taylor series expansion of the delayed term. In a second time, a mixed approach is proposed to predict effectively the real critical time delay of autonomous controlled systems subjected to friction-induced vibration. The efficiency of the proposed approach is illustrated by numerical examples for the prediction of self-sustaining vibrations of a phenomenological model with two degrees of freedom for which it is possible to provide a clear understanding and illustration of the phenomena involved and observed.