We give an overview of how the Riccati equation makes its appearance in the stability analysis of linear systems with delays. We avoid complexities as time-invariance, added perturbations, distributed delays etc, to get to the main issues. Most generalizations can be or have been carried out, but do not add substantially to our understanding. We also show the connection between quadratic stabil...

Stability of Time-Delay Systems by Keqin Gu, Vladimir L. Kharitonov, and Jie Chen, Birkhäuser, 2003, 353 pp., ISBN 0-8176-4212-9, $79.95. Reviewed by Vladimir Rasvan and Dan Popescu. The destabilizing effects of time delays are well known to control engineers. In fact, robustness against time delay has been an important and challenging problem from the earliest days of classical control. The la...

This paper investigates the observer-based adaptive stabilization control problem for a class of time-delay nonlinear systems with unknown gain using an echo state network (ESN). In order to handle functions, new recurrent neural (RNN) approximation method called ESN is utilized. It improves accuracy, reduces computing cost, and simple train. To address issue gain, Nussbaum function used, Lyapu...

A new (descriptor) model transformation and a corresponding Lyapunov–Krasovskii functional are introduced for stability analysis of systems with delays. Delay-dependent=delay-independent stability criteria are derived for linear retarded and neutral type systems with discrete and distributed delays. Conditions are given in terms of linear matrix inequalities and for the 1rst time refer to neutr...

The article analyzes a linear mechanical system with large parameter at the vector of velocity forces and distributed delay in positional forces. With aid decomposition method, conditions are obtained under which problem stability analysis original second-order differential equations can be reduced to studying two auxiliary first-order subsystems. It should noted that one subsystems does not co...

This paper examines the problem of improved fixed-time stability for generalized delayed fractional-order systems (FOSs). As a first step, some conditions are presented in two theorems to verify (F-TS) FOSs by using Lyapunov theory and indefinite functionals, where derivative functions may not exist. Furthermore, corresponding estimated settling time is also provided. Second, results extended s...

The attacks on power systems have been happening all the time, and gradually changing from a single attack to hybrid multiple cyber attacks. Such may cause more catastrophic damages security safety of multi-area systems. Here, control problem is analyzed for under Two Lyapunov–Krasovskii functionals are constructed, by utilizing second-order canonical Bessel–Legendre inequality, sufficient cond...

Robustness is established for the predictor feedback for linear time-invariant systems with respect to possibly time-varying perturbations of the input delay, with a constant nominal delay. The prior results have addressed qualitatively constant delay perturbations (robustness of stability in L2 norm of actuator state) and delay perturbations with restricted rate of change (robustness of stabil...

Robust stability and the guaranteed cost control problem are considered for discrete-time systems with time-varying delays from given intervals. A new construction of Lyapunov– Krasovskii functionals (LKFs), which has been recently introduced in the continuous-time case, is applied. To a nominal LKF, which is appropriate to the system with nominal delays, terms are added that correspond to the ...

In this article, we are interested in analysing stability of systems that incorporate time-varying delays in their dynamic. The Lyapunov-Krasovskii approach is definitely the most popular method to address this issue and many results have proposed new functionals and enhanced techniques for deriving less conservative stability conditions. In this present work, we propose an original approach: t...