Delay-dependent exponential stability of neutral stochastic delay systems

This paper studies stability of neutral stochastic delay systems by linear matrix inequality (LMI) approach. Delay dependent criterion for exponential stability is presented and numerical examples are conducted to verify the effectiveness of the proposed method

A novel delay-dependent asymptotic stability conditions for differential and Riemann-Liouville fractional differential neutral systems with constant delays and nonlinear perturbation

The novel delay-dependent asymptotic stability of a differential and Riemann-Liouville fractional differential neutral system with constant delays and nonlinear perturbation is studied. We describe the new asymptotic stability criterion in the form of linear matrix inequalities (LMIs), using the application of zero equations, model transformation and other inequalities. Then we show the new delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral system with constant delays. Furthermore, we not only present the improved delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral system with single constant delay but also the new delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral equation with constant delays. Numerical examples are exploited to represent the improvement and capability of results over another research as compared with the least upper bounds of delay and nonlinear perturbation.This work is supported by Science Achievement Scholarship of Thailand (SAST), Research and Academic Affairs Promotion Fund, Faculty of Science, Khon Kaen University, Fiscal year 2020 and National Research Council of Thailand and Khon Kaen University, Thailand (6200069)

A novel delay-dependent asymptotic stability conditions for differential and Riemann-Liouville fractional differential neutral systems with constant delays and nonlinear perturbation

The novel delay-dependent asymptotic stability of a differential and Riemann-Liouville fractional differential neutral system with constant delays and nonlinear perturbation is studied. We describe the new asymptotic stability criterion in the form of linear matrix inequalities (LMIs), using the application of zero equations, model transformation and other inequalities. Then we show the new delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral system with constant delays. Furthermore, we not only present the improved delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral system with single constant delay but also the new delay-dependent asymptotic stability criterion of a differential and Riemann-Liouville fractional differential neutral equation with constant delays. Numerical examples are exploited to represent the improvement and capability of results over another research as compared with the least upper bounds of delay and nonlinear perturbation.This work is supported by Science Achievement Scholarship of Thailand (SAST), Research and Academic Affairs Promotion Fund, Faculty of Science, Khon Kaen University, Fiscal year 2020 and National Research Council of Thailand and Khon Kaen University, Thailand (6200069)

Delay-dependent exponential stability of neutral stochastic delay systems (vol 54, pg 147, 2009)

In the above titled paper originally published in vol. 54, no. 1, pp. 147-152) of IEEE Transactions on Automatic Control, there were some typographical errors in inequalities. Corrections are presented here

Stability of Neutral Delay Differential Equations and Their Discretizations

Disertační práce se zabývá asymptotickou stabilitou zpožděných diferenciálních rovnic a jejich diskretizací. V práci jsou uvažovány lineární zpožděné diferenciální rovnice s~konstantním i neohraničeným zpožděním. Jsou odvozeny nutné a postačující podmínky popisující oblast asymptotické stability jak pro exaktní, tak i diskretizovanou lineární neutrální diferenciální rovnici s konstantním zpožděním. Pomocí těchto podmínek jsou porovnány oblasti asymptotické stability odpovídajících exaktních a diskretizovaných rovnic a vyvozeny některé vlastnosti diskrétních oblastí stability vzhledem k měnícímu se kroku použité diskretizace. Dále se zabýváme lineární zpožděnou diferenciální rovnicí s neohraničeným zpožděním. Je uveden popis jejích exaktních a diskrétních oblastí asymptotické stability spolu s asymptotickým odhadem jejich řešení. V závěru uvažujeme lineární diferenciální rovnici s více neohraničenými zpožděními.The doctoral thesis discusses the asymptotic stability of delay differential equations and their discretizations. The linear delay differential equations with constant as well as infinite lag are considered. The necessary and sufficient conditions describing the asymptotic stability region of both exact and discretized linear neutral delay differential equation with constant lag are derived. We compare asymptotic stability domains of corresponding exact and discretized equations and discuss properties of derived stability regions with respect to a changing stepsize of the utilized discretization. Further, we investigate the linear delay differential equation with the infinite lag. We present the description of its exact and discrete asymptotic stability regions together with asymptotic estimates of its solutions. The linear delay differential equation with several infinite lags is discussed as well.

Stability analysis and observer design for neutral delay systems

Copyright [2002] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This paper deals with the observer design problem for a class of linear delay systems of the neutral-type. The problem addressed is that of designing a full-order observer that guarantees the exponential stability of the error dynamic system. An effective algebraic matrix equation approach is developed to solve this problem. In particular, both the observer analysis and design problems are investigated. By using the singular value decomposition technique and the generalized inverse theory, sufficient conditions for a neutral-type delay system to be exponentially stable are first established. Then, an explicit expression of the desired observers is derived in terms of some free parameters. Furthermore, an illustrative example is used to demonstrate the validity of the proposed design procedur