### Details

#### Title

Lyapunov functional for a linear system with two delays both retarded and neutral type#### Journal title

Archives of Control Sciences#### Yearbook

2010#### Numer

No 1#### Publication authors

#### Divisions of PAS

Nauki Techniczne#### Description

Archives of Control Sciences welcomes for consideration papers on topics of significance in broadly understood control science and related areas, including: basic control theory, optimal control, optimization methods, control of complex systems, mathematical modeling of dynamic and control systems, expert and decision support systems and diverse methods of knowledge modelling and representing uncertainty (by stochastic, set-valued, fuzzy or rough set methods, etc.), robotics and flexible manufacturing systems. Related areas that are covered include information technology, parallel and distributed computations, neural networks and mathematical biomedicine, mathematical economics, applied game theory, financial engineering, business informatics and other similar fields.

Aims and Scope: Archives of Control Sciences publishes papers in the broadly understood field of control science and related areas while promoting the closer integration of the Polish, as well as other Central and East European scientific communities with the international world of science.

#### Publisher

Committee of Automatic Control and Robotics PAS#### Date

2010#### Identifier

ISSN 1230-2384#### References

J. Duda: Parametric optimization problem for systems with time delay. PhD thesis, AGH University of Science and Technology, Krakow, Poland, 1986. ; Duda J. (1988), Parametric optimization of neutral linear system with respect to the general quadratic performance index, Archiwum Automatyki i Telemechaniki, 33, 448. ; Duda J. (2009), Lyapunov functional for a linear system with two delays, Control and Cybernetics. ; Fridman E. (2001), New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems, Systems & Control Letters, 43, 309. ; Górecki H. (1989), Analysis and synthesis of time delay systems. ; Gu K. (1997), Discretized LMI set in the stability problem of linear time delay systems, Int. J. of Control, 68, 923. ; Gu K. (2009), Lyapunov-Krasovskii functional for uniform stability of coupled differential-functional equations, Automatica, 45, 798. ; Han Q. (2004), On robust stability of neutral systems with time-varying discrete delay and norm-bounded uncertainty, Automatica, 40, 1087. ; Han Q. (2004), A descriptor system approach to robust stability of uncertain neutral systems with discrete and distributed delays, Automatica, 40, 1791. ; Han Q. (2005), On stability of linear neutral systems with mixed time delays: A discretised Lyapunov functional approach, Automatica, 41, 1209. ; Han Q. (2009), Discrete delay decomposition approach to stability of linear retarded and neutral system, Automatica, 45, 517. ; Infante E. (1978), A Liapunov functional for a matrix difference-differential equation, J. Differential Equations, 29, 439. ; Ivanescu D. (2003), On delay-dependent stability for linear neutral systems, Automatica, 39, 255. ; Kharitonov V. (2005), Lyapunov functionals and Lyapunov matrices for neutral type time delay systems: a single delay case, Int. J. of Control, 78, 783. ; Kharitonov V. (2008), Lyapunov matrices for a class of neutral type time delay systems, Int. J. of Control, 81, 883. ; Kharitonov V. (2004), Exponential estimates for time delay systems, Systems & Control Letters, 53, 395. ; Kharitonov V. (null), Lyapunov matrices for time-delay systems, Systems & Control Letters, 55, 2006, 697. ; Kharitonov V. (2003), Lyapunov-Krasovskii approach to the robust stability analysis of time-delay systems, Automatica, 39, 15. ; Repin Yu. (1965), Quadratic Lyapunov functionals for systems with delay, Prikl. Mat. Mekh, 29, 564.#### DOI

10.2478/v10170-010-0006-7