### 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#### Authors

#### Divisions of PAS

Nauki Techniczne#### 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