Improved results on stability and stabilization criteria for uncertain linear systems with time-varying delays

References

• S. Boyd, L.E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, 1994.
   Google Scholar
• C. Briat, Convergence and equivalence results for the Jensen's inequality-application to time-delay and sampled-data systems, IEEE Trans. Autom. Control 56 (2011), pp. 1660–1665.
   Web of Science ®Google Scholar
• M.C. de Oliveira and R.E. Skelton, Stability Tests for Constrained Linear Systems, Springer, Berlin, 2001, pp. 241–257.
   Google Scholar
• R. Dey, S. Ghosh, G. Ray, and A. Rakshit, State feedback stabilization of uncertain linear time-delay systems: A nonlinear matrix inequality approach, Numer. Linear Algebra Appl. 18 (2011), pp. 351–361.
   Web of Science ®Google Scholar
• E. Fridman and U. Shaked, An improved stabilization method for linear time-delay systems, IEEE Trans. Autom. Control 47 (2002), pp. 1931–1937.
   Web of Science ®Google Scholar
• K. Gu, A further refinement of discretized Lyapunov functional method for the stability of time-delay systems, Int. J. Control 74 (2001), pp. 967–976.
   Web of Science ®Google Scholar
• É. Gyurkovics, A note on Wirtinger-type integral inequalities for time-delay systems, Automatica 61 (2015), pp. 44–46.
   Web of Science ®Google Scholar
• Y. He, Q.-G. Wang, C. Lin, and M. Wu, Delay-range-dependent stability for systems with time-varying delay, Automatica 43 (2007), pp. 371–376.
   Web of Science ®Google Scholar
• L.V. Hien and H. Trinh, An enhanced stability criterion for time-delay systems via a new bounding technique, J. Frankl. Inst. 352 (2015), pp. 4407–4422.
   Web of Science ®Google Scholar
• C. Jeong, P. Park, and S.H. Kim, Improved approach to robust stability and H∞ performance analysis for systems with an interval time-varying delay, Appl. Math. Comput. 218 (2012), pp. 10533–10541.
   Web of Science ®Google Scholar
• J.-H. Kim, Note on stability of linear systems with time-varying delay, Automatica 47 (2011), pp. 2118–2121.
   Web of Science ®Google Scholar
• J.-H. Kim, Further improvement of Jensen inequality and application to stability of time-delayed systems, Automatica 64 (2016), pp. 121–125.
   Web of Science ®Google Scholar
• S.H. Kim, P. Park, and C.K. Jeong, Robust H∞ stabilisation of networks control systems with packet analyser, IET Control Theory Appl. 4 (2010), pp. 1828–1837.
   Web of Science ®Google Scholar
• J.W. Ko and P.G. Park, Delay-dependent stability criteria for systems with asymmetric bounds on delay derivative, J. Frankl. Inst. 348 (2011), pp. 2674–2688.
   Web of Science ®Google Scholar
• O.M. Kwon, J.H. Park, S.M. Lee, and E.J. Cha, New augmented Lyapunov–Krasovskii functional approach to stability analysis of neural networks with time-varying delays, Nonlinear Dyn. 76 (2014), pp. 221–236.
   Web of Science ®Google Scholar
• O.M. Kwon, M.J. Park, J.H. Park, S.M. Lee, and E.J. Cha, Stability and H∞ performance analysis for Markovian jump systems with time-varying delays, J. Frankl. Inst. 351 (2014), pp. 4724–4748.
   Web of Science ®Google Scholar
• O.M. Kwon, M.J. Park, J.H. Park, S.M. Lee, and E.J. Cha, Improved results on stability of linear systems with time-varying delays via Wirtinger-based integral inequality, J. Frankl. Inst. 351 (2014), pp. 5386–5398.
   Web of Science ®Google Scholar
• Y.S. Lee, Y.S. Moon, and W.H. Kwon, Delay-dependent Guaranteed Cost Control for Uncertain State-delayed Systems, Proceedings of American Control Conference, Arlington, USA, 2001, pp. 3376–3381.
   Google Scholar
• W.I. Lee, S.Y. Lee, and P.G. Park, Improved criteria on robust stability and H∞ performance for linear systems with interval time-varying delays via new triple integral functionals, Appl. Math. Comput. 243 (2014), pp. 570–577.
   Web of Science ®Google Scholar
• T. Li, L. Guo, and Y. Zhang, Delay-range-dependent robust stability and stabilization for uncertain systems with time-varying delay, Int. J. Robust Nonlinear Control 18 (2008), pp. 1372–1387.
   Web of Science ®Google Scholar
• Y. Liu, W. Ma, M.S. Mahmoud, and S.M. Lee, Improved delay-dependent exponential stability criteria for neutral-delay systems with nonlinear uncertainties, Appl. Math. Model. 39 (2015), pp. 3164–3174.
   Web of Science ®Google Scholar
• Y.S. Moon, P.G. Park, W.H. Kwon, and Y.S. Lee, Delay-dependent robust stabilization of uncertain state-delayed systems, Int. J. Control 74 (2001), pp. 1447–1455.
   Web of Science ®Google Scholar
• S.I. Niculescu, Delay Effects on Stability: A Robust Control Approach, Springer, Berlin, 2001.
   Google Scholar
• P.G. Park and J.W. Ko, Stability and robust stability for systems with a time-varying delay, Automatica 43 (2007), pp. 1855–1858.
   Web of Science ®Google Scholar
• P.G. Park, J.W. Ko, and C. Jeong, Reciprocally convex approach to stability of systems with time-varying delays, Automatica 47 (2011), pp. 235–238.
   Web of Science ®Google Scholar
• P.G. Park, W.I. Lee, and S.Y. Lee, Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems, J. Frankl. Inst. 352 (2015), pp. 1378–1396.
   Web of Science ®Google Scholar
• M.N.A. Parlakçı, Improved robust stability criteria and design of robust stabilizing controller for uncertain linear time-delay systems, Int. J. Robust Nonlinear Control 16 (2006), pp. 599–636.
   Web of Science ®Google Scholar
• J.-P. Richard, Time-delay systems: An overview of some recent advances and open problems, Automatica 39 (2003), pp. 1667–1694.
   Web of Science ®Google Scholar
• A. Seuret and F. Gouaisbaut, Wirtinger-based integral inequality: Application to time-delay systems, Automatica 49 (2013), pp. 2860–2866.
   Web of Science ®Google Scholar
• J. Sun, G.P. Liu, and J. Chen, Delay-dependent stability and stabilization of neutral time-delay systems, Int. J. Robust Nonlinear Control 15 (2009), pp. 1364–1375.
   Web of Science ®Google Scholar
• J. Sun, G.P. Liu, J. Chen, and D. Rees, Improved delay-range-dependent stability criteria for linear systems with time-varying delays, Automatica 46 (2010), pp. 466–470.
   Web of Science ®Google Scholar
• J. Sun, Q.-L. Han, J. Chen, and G.-P. Liu, Less conservative results on stability for linear systems with a time-varying delay, Optimal Control Appl. Methods 34 (2013), pp. 670–679.
   Web of Science ®Google Scholar
• M. Wu, Y. He, and J.-H. She, New delay-dependent stability criteria and stabilizing method for neutral systems, IEEE Trans. Autom. Control 49 (2004), pp. 2266–2271.
   Web of Science ®Google Scholar
• H.-B. Zeng, Y. He, M. Wu, and J. She, Free-matrix-based integral inequality for stability analysis of systems with time-varying delay, IEEE Trans. Autom. Control 60 (2015), pp. 2768–2772.
   Web of Science ®Google Scholar
• H.-B. Zeng, Y. He, M. Wu, and J. She, New results on stability analysis for systems with discrete distributed delay, Automatica 60 (2015), pp. 189–192.
   Web of Science ®Google Scholar
• C.-K. Zhang, Y. He, L. Jiang, and M. Wu, Stability analysis for delayed neural networks considering both conservativeness and complexity, IEEE Trans. Neural Netw. Learn. Syst. doi: 10.1109/TNNLS.2015.2449898.
   Web of Science ®Google Scholar