By using the average dwell time approach, we identify a class of switching signals to guarantee exponential stability and L2 gain of the switched linear system with interval time-varying delay excluding zero. By taking both the lower bound and upper bound of delay into consideration in the chosen Lyapunov function, several new stability criteria are presented in terms of linear matrix inequalities. Compared with some results in the literature, it is theoretically established that our results are less restrictive.
Inspec keywords: delays; asymptotic stability; time-varying systems; linear matrix inequalities; Lyapunov methods; linear systems
Other keywords:
Subjects: Stability in control theory; Algebra; Distributed parameter control systems; Time-varying control systems
References
-
-
1)
- S. Kim , S.A. Campbell , X. Liu . Stability of a class of linear switching systems with time delay. IEEE Trans. Circuits syst. I , 384 - 393
-
2)
- J. Hale , Verduyn , S.M. Lunel . (1993) Introduction to functional differential equations.
-
3)
- S. Boyd , L.El Ghaoui , E. Feron , V. Balakrishnan . (1994) Linear matrix inequality in system and control theory: studies in applied mathematics.
-
4)
- L. Hetel , J. Daafouz , C. Iung . Stabilization of arbitrary switched linear systems with unknown time-varying delays. IEEE Trans. Automatic Control , 10 , 1668 - 1674
-
5)
- Sun, X.M., Dimirovski, G.M., Zhao, J., Wang, W.: `Exponential stability for switched delay systems based on average dwell time technique and Lyapunov function method', Proc. American Control Conf., 2006, p. 1539–1543.
-
6)
- R.A. DeCarlo , M.S. Branicky , S. Pettersson , B. Lennartson . Perspectives and results on the stability and stabilizability of hybrid systems. Proc. IEEE , 7 , 1069 - 1082
-
7)
- K.S. Narendra , J. Balakrishnan . Adaptive control using multiple models. IEEE Trans. Autom. Control , 2 , 171 - 187
-
8)
- Kulkarni, V., Jun, M., Hespanha, J.: `Piecewise quadratic Lyapunov functions for piecewise affine time-delay systems', Proc. American Control Conf., 2004, Boston, p. 3885–3889.
-
9)
- J.A.D. Appleby , I. Gyori , D.W. Reynolds . On exact rates of decay of solutions of linear systems of Volterra equations with delay. J. Math. Anal. Appl. , 1 , 56 - 77
-
10)
- X.M. Sun , J. Zhao . Robust exponential stability of linear switched delay systems: an average dwell time method. Dyn. Continuous Discrete Impul. Syst. B , 209 - 221
-
11)
- D. Liberzon , A.S. Morse . Basic problems in stability and design of switched systems. IEEE Control Syst. Mag. , 5 , 59 - 70
-
12)
- D.K. Kim , P.G. Park , J.W. Ko . Output-feedback H∞ control of systems over communication networks using a deterministic switching system approach. Automatica , 1205 - 1212
-
13)
- Xie, G., Wang, L.: `Stability and stabilization of switched linear systems with state delay: continuous-time case', The 16th Mathematical Theory of Networks and Systems Conf., 2004, Catholic University of Leuven.
-
14)
- Sun, Y.G., Wang, L., Xie, G.: `Stabilization of switched linear systems with multiple time-varying delays', Proc. 45th IEEE Conf. Decision and Control, 2006, San Diego, p. 4070–4075.
-
15)
- Zhai, G., Sun, Y., Chen, X., Anthony, X.N.M.: `Stability and ', Proc. American Control Conf., 2003, Denver, p. 2682–2687.
-
16)
- Z. Ji , X. Guo , S. Xu , L. Wang . Stabilization of switched linear systems with time-varying delay in switching occurence detection. Circuits Syst. Signal Process. , 3 , 361 - 367
-
17)
- J. Tlusty . (1985) Machine dynamics, in handbook of high speed machining technology.
-
18)
- M. De la Sen . Quadratic stability and stabilisation of switched dynamic systems with uncommensurate internal point delays. Appl. Math. Comput. , 1 , 508 - 526
-
19)
- W.P. Dayawansa , C.F. Martin . A converse Lyapunov theorem for a class of dynamical systems which undergo switching. IEEE Trans. Autom. Control , 751 - 760
-
20)
- M.A. Wicks , P. Peleties , R.A. DeCarlo . Switched controller synythesis for the quadratic stabilization of a pair of unstable linear systems. Eur. J. Control , 140 - 147
-
21)
- Zhao, J., Hill, D.J.: `On stability and ', Proc. 44th IEEE Conf. Decision and Control, 2005, Seville, p. 3279–3284.
-
22)
- S.L. Niculescu . (2001) Delay effects on stability: a robust control approach.
-
23)
- A. Morse . Supervisory control of families of linear set-point controllers – part 1: exact matching. IEEE Trans. Autom. Control , 10 , 1413 - 1431
-
24)
- C.R. Knospe , M. Roozbehani . Stability of linear systems sixth interval time delays excluding zero. IEEE Trans. Autom. Control , 1271 - 1288
-
25)
- A.M. Annaswamy , M. Fleifil , J.P. Hathout , A.F. Ghoniem . Impact of linear coupling on the design of active controllers for thermoacoustic instability. Combust. Sci. Technol. , 131 - 160
-
26)
- M. Sun , J. Zhao , D.J. Hill . Stability and ℒ2 gain for switched delay systems: a delay-dependent method. Automatica , 10 , 1769 - 1774
-
27)
- J.P. Richard . Time-delay systems: an overview of some recent advances and open problems. Automatica , 1667 - 1694
-
28)
- A.N. Michel , G.S. Zhai , X.K. Chen . L∞ gain analysis of switched symmetric systems with time delays. Dyn. Continuous Discrete Impul. Syst. A , 219 - 232
-
29)
- C. Meyer , S. Schroder , R.W. De Doncker . Solid-state circuit breakers and current limiters for medium-voltage systems having distributed power systems. IEEE Trans. Power Electron. , 1333 - 1340
-
1)
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2008.0162
Related content
content/journals/10.1049/iet-cta.2008.0162
pub_keyword,iet_inspecKeyword,pub_concept
6
6