Exponential-weighted input-to-state stability of hybrid impulsive switched systems

Stability of the non-linear systems with external inputs is an important problem in control theory and engineering. Input-to-state stability (ISS) is one of the stability concepts that have been introduced to non-linear systems. This study extends the ISS to a more general case, namely, exponential-weighted input-to-state stability (eλt-weighted ISS). By employing the Lyapunov function and Lyapunov–Razumikhin techniques, eλt-weighted ISS is proposed and studied for the impulsive switched hybrid systems with and without time delay. An example and simulation results are given to illustrate the effectiveness of the obtained theoretical results.

[1]  David J. Hill,et al.  Input-to-state stability for discrete time-delay systems via the Razumikhin technique , 2009, Syst. Control. Lett..

[2]  Eduardo Sontag.  Smooth stabilization implies coprime factorization , 1989, IEEE Transactions on Automatic Control.

[3]  Andrea Serrani,et al.  Adaptive feedforward disturbance rejection in nonlinear systems , 2009, Syst. Control. Lett..

[4]  Eduardo Sontag.  Comments on integral variants of ISS , 1998 .

[5]  Z. Guan,et al.  Stabilization of complex network with hybrid impulsive and switching control , 2008 .

[6]  A. Morse,et al.  Stability of switched systems with average dwell-time , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[7]  G. Hu,et al.  Mean-square Exponential Input-to-state Stability of Euler-Maruyama Method Applied to Stochastic Control Systems , 2010 .

[8]  Zhi-Hong Guan,et al.  Stability analysis on uncertain stochastic impulsive systems with time-delay , 2008 .

[9]  Hyungbo Shim,et al.  Switching adaptive output feedback model predictive control for a class of input-constrained linear plants , 2008 .

[10]  Wei Xing Zheng,et al.  Novel stability of cellular neural networks with interval time-varying delay , 2008, Neural Networks.

[11]  Dragan Nesic,et al.  Power characterizations of input-to-state stability and integral input-to-state stability , 2001, IEEE Trans. Autom. Control..

[12]  Zhong-Ping Jiang,et al.  Input-to-state stability of hybrid switched systems with impulsive effects , 2008, 2008 7th World Congress on Intelligent Control and Automation.

[13]  Zhengguo Li,et al.  Input-to-state stabilization of switched nonlinear systems , 2001, IEEE Trans. Autom. Control..

[14]  J. Tsinias,et al.  Notions of exponential robust stochastic stability, ISS and their Lyapunov characterizations , 2003 .

[15]  Wei Xing Zheng,et al.  Input-to-state stability and integral input-to-state stability of nonlinear impulsive systems with delays , 2009, Autom..

[16]  Guangdeng Zong,et al.  Exponential stability of switched systems with impulsive effect , 2005 .

[17]  P. Li,et al.  Stabilisation and synchronisation of chaotic systems via hybrid control , 2007 .

[18]  João Pedro Hespanha,et al.  Supervision of integral-input-to-state stabilizing controllers , 2002, Autom..

[19]  E. Boukas,et al.  Stability and robust stabilisation for uncertain discrete stochastic hybrid singular systems with time delay , 2009 .

[20]  Debasish Chatterjee,et al.  Input-to-state stability of switched systems and switching adaptive control , 2007, Autom..

[21]  Mean-square Exponential Input-to-state Euler-Maruyama Method Applied to Stochastic Control Systems: Mean-square Exponential Input-to-state Euler-Maruyama Method Applied to Stochastic Control Systems , 2010 .

[22]  Wu‐Hua Chen,et al.  Mean square exponential stability of uncertain stochastic delayed neural networks , 2008 .

[23]  Chaohong Cai,et al.  Input-output-to-state stability for discrete-time systems , 2008, Autom..

[24]  V. Lakshmikantham,et al.  Theory of Impulsive Differential Equations , 1989, Series in Modern Applied Mathematics.

[25]  Yongkun Li,et al.  Exponential stability of fuzzy Cohen–Grossberg neural networks with time delays and impulsive effects☆ , 2010 .

[26]  Ming Wang,et al.  A remark on exponential stability of time-delayed Burgers equation , 2009 .

[27]  Integral input-to-state stability of nonlinear control systems with delays , 2007 .

[28]  D. Liberzon,et al.  On Input-to-State Stability of Impulsive Systems , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[29]  Xuemin Shen,et al.  On hybrid impulsive and switching systems and application to nonlinear control , 2005, IEEE Transactions on Automatic Control.