A new delay-dependent exponential stability criterion for Itô stochastic systems with Markovian switching and time-varying delay

References

• Benjelloun , K and Boukas , EK . 1998 . Mean Square Stochastic Stability of Linear Time-delay Systems with Markovian Jumping Parameters . IEEE Transactions on Automatic Control , 43 : 1456 – 1460 .
   Web of Science ®Google Scholar
• Elliott , RJ . 1982 . Stochastic Calculus and Applications , New York : Springer-Verlag .
   Google Scholar
• Gu , K . 1997 . Discretized LMI Set in the Stability Problem of Linear Uncertain Time-delay Systems . International Journal Control , 68 : 923 – 934 .
   Web of Science ®Google Scholar
• Guan , ZH , Chen , WH and Xu , JX . 2005 . Delay-dependent Stability and Stabilizability of Uncertain Jump Bilinear Stochastic Systems with Mode-dependent Time-delays . International Journal Systems Science , 36 : 275 – 285 .
   Web of Science ®Google Scholar
• Jumarie , G . 1988 . Simple General Method to Analyse the Moment Stability and Sensitivity of Non-linear Stochastic Systems with or without Delay . International Journal Systems Science , 19 : 111 – 124 .
   Web of Science ®Google Scholar
• Kolmanovskii , VB and Nosov , VR . 1986 . Stability of Functional Differential Equations , London : Academic Press .
   Google Scholar
• He , Y , Wang , QG , Xie , L and Lin , C . 2007 . Further Improvement of Free-weighting Matrices Techniques for Systems with Time-varying Delay . IEEE Transactions on Automatic Control , 52 : 293 – 299 .
   Web of Science ®Google Scholar
• Lu , CY , Tsai , JSH , Jong , GJ and Su , TJ . 2003 . An LMI-based Approach for Robust Stabilization of Uncertain Stochastic Systems with Time-varying Delays . IEEE Transactions on Automatic Control , 48 : 286 – 289 .
   Web of Science ®Google Scholar
• Mao , X . 1994 . Exponential Stability of Stochastic Differential Equations , New York : Marcel Dekker .
   Google Scholar
• Mao , X . 2002 . Exponential Stability of Stochastic Delay Interval Systems with Markovian Switching . IEEE Transactions on Automatic Control , 47 : 1604 – 1612 .
   Web of Science ®Google Scholar
• Moon , YS , Park , P , Kwon , WH and Lee , YS . 2001 . Delay-dependent Robust Stabilization of Uncertain State-delayed Systems . International Journal Control , 74 : 1447 – 1455 .
   Web of Science ®Google Scholar
• Park , GS , Choi , HL and Lim , JT . 2008 . On Stability of Linear Time-delay Systems with Multiple Delays . International Journal Systems Science , 39 : 839 – 852 .
   Web of Science ®Google Scholar
• Park , P and Ko , JW . 2007 . Stability and Robust Stability for Systems with a Time-varying Delay . Automatica , 43 : 1855 – 1858 .
   Web of Science ®Google Scholar
• Sun , M , Lam , J , Xu , S and Zou , Y . 2007 . Robust Exponential Stabilization for Markovian Jump Systems with Mode-dependent Input Delay . Automatica , 43 : 1799 – 1807 .
   Web of Science ®Google Scholar
• Wu , J , Chen , T and Wang , L . 2006 . Delay-dependent Robust Stability and H ∞ Control for Jump Linear Systems with Delays . Systems & Control Letters , 55 : 939 – 948 .
   Web of Science ®Google Scholar
• Xu , S and Chen , T . 2002 . Robust H ∞ Control for Uncertain Stochastic Systems with State Delay . IEEE Transactions on Automatic Control , 47 : 2089 – 2094 .
   Web of Science ®Google Scholar
• Xu , S , Chu , Y , Lu , J and Lam , J . 2006 . Exponential Dynamical Output Feedback Controller Design for Stochastic Neutral Systems with Distributed Delays . IEEE Transactions on Systems, Man and Cybernetics , 36 : 540 – 548 .
   Web of Science ®Google Scholar
• Xu , S and Lam , J . 2007 . On Equivalence and Efficiency of Certain Stability Criteria for Time-delay Systems . IEEE Transactions on Automatic Control , 52 : 95 – 105 .
   Web of Science ®Google Scholar
• Yuan , C and Lygeros , J . 2006 . Asymptotic Stability and Boundedness of Delay Switching Diffusions . IEEE Transactions on Automatic Control , 51 : 171 – 175 .
   Web of Science ®Google Scholar
• Yue , D and Han , QL . 2005 . Delay-dependent Exponential Stability of Stochastic Systems with Time-varying Delay, Nonlinearity Markovian Switching . IEEE Transactions on Automatic Control , 50 : 217 – 222 .
   Web of Science ®Google Scholar
• Zhang , B , Zhou , S and Xu , S . 2007 . Delay-dependent H ∞ Controller Design for Linear Neutral Systems with Discrete and Distributed Delays . International Journal Systems Science , 38 : 611 – 621 .
   Web of Science ®Google Scholar