Exponential stability of nonlinear impulsive switched systems with stable and unstable subsystems

Exponential stability and robust exponential stability relating to switched systems consisting of stable and unstable nonlinear subsystems are considered in this study. At each switching time instant, the impulsive increments which are nonlinear functions of the states are extended from switched linear systems to switched nonlinear systems. Using the average dwell time method and piecewise Lyapunov function approach, when the total active time of unstable subsystems compared to the total active time of stable subsystems is less than a certain proportion, the exponential stability of the switched system is guaranteed. The switching law is designed which includes the average dwell time of the switched system. Switched systems with uncertainties are also studied. Sufficient conditions of the exponential stability and robust exponential stability are provided for switched nonlinear systems. Finally, simulations show the effectiveness of the result.

[1]  M. De la Sen,et al.  A note on the stability of linear time-delay systems with impulsive inputs , 2003 .

[2]  Kazumine Moriyasu.  A note on Ω-stability , 1991 .

[3]  Wei Zhu.  Stability analysis of switched impulsive systems with time delays , 2010 .

[4]  Raymond A. DeCarlo,et al.  Switched Controller Synthesis for the Quadratic Stabilisation of a Pair of Unstable Linear Systems , 1998, Eur. J. Control.

[5]  Kok Lay Teo,et al.  Exponential Stability With $L_{2}$-Gain Condition of Nonlinear Impulsive Switched Systems , 2010, IEEE Transactions on Automatic Control.

[6]  J. Imae,et al.  gain analysis for switched systems with continuous-time and discrete-time subsystems , 2005 .

[7]  Wei Wang,et al.  Stability Analysis for Linear Switched Systems With Time-Varying Delay , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[8]  Yong-Hua Song,et al.  The theory of hybrid control systems and its application perspective in electric power systems , 2001, 2001 International Conferences on Info-Tech and Info-Net. Proceedings (Cat. No.01EX479).

[9]  N. C. State,et al.  Stability Analysis , 2019, Converter-Interfaced Energy Storage Systems.

[10]  K. Teo,et al.  Robust H∞ stabilisation with definite attenuance of an uncertain impulsive switche system , 2005, The ANZIAM Journal.

[11]  Bonaventure Intercontinental,et al.  ON DECISION AND CONTROL , 1985 .

[12]  Wei Wang,et al.  Stability analysis and L2-gain of switched delay systems with stable and unstable subsystems , 2007, 2007 IEEE 22nd International Symposium on Intelligent Control.

[13]  Ian R. Petersen,et al.  A riccati equation approach to the stabilization of uncertain linear systems , 1986, Autom..

[14]  V. M. Marchenko,et al.  Representation of solutions of control hybrid differential-difference impulse systems , 2009 .

[15]  Xinzhi Liu,et al.  Robust Stability Analysis of Guaranteed Cost Control for Impulsive Switched Systems , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[16]  Shengyuan Xu,et al.  Robust H∞ stabilization for uncertain switched impulsive control systems with state delay: An LMI approach , 2008 .

[17]  Bengt Lennartson,et al.  Hybrid systems in process control , 1996 .

[18]  Ian A. Hiskens,et al.  Stability of hybrid system limit cycles: application to the compass gait biped robot , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[19]  Horacio J. Marquez,et al.  Controllability and Observability for a Class of Controlled Switching Impulsive Systems , 2008, IEEE Transactions on Automatic Control.

[20]  Daniel Liberzon,et al.  Switching in Systems and Control , 2003, Systems & Control: Foundations & Applications.

[21]  E. Evangelisti.  Controllability and Observability , 2011 .

[22]  Pravin Varaiya,et al.  Smart cars on smart roads: problems of control , 1991, IEEE Trans. Autom. Control..

[23]  Jian Chen,et al.  MAGDM Linear-Programming Models With Distinct Uncertain Preference Structures , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[24]  Xinzhi Liu,et al.  Stability of a class of linear switching systems with time delay , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[25]  João Pedro Hespanha,et al.  Lyapunov conditions for input-to-state stability of impulsive systems , 2008, Autom..

[26]  Barbara Hayes-Roth,et al.  Intelligent Control , 1994, Artif. Intell..

[27]  M. De la Sen,et al.  Stability of impulsive time-varying systems and compactness of the operators mapping the input space into the state and output spaces , 2006 .

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

[29]  Daniel W. C. Ho,et al.  Stability, robust stabilization and H∞ control of singular-impulsive systems via switching control , 2006, Syst. Control. Lett..

[30]  Mi Friswell,et al.  17th IFAC World Congress , 2008 .

[31]  Bo Hu,et al.  Disturbance attenuation properties of time-controlled switched systems , 2001, J. Frankl. Inst..

[32]  A. Michel,et al.  Stability analysis of switched systems with stable and unstable subsystems: an average dwell time approach , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[33]  Xinzhi Liu,et al.  Input-to-state stability of impulsive and switching hybrid systems with time-delay , 2011, Autom..

[34]  Kalyana R. Kantipudi.  Controllability and Observability , 2005 .

[35]  Georgi M. Dimirovski,et al.  Average Dwell-time Method to Stabilization and L2-gain Analysis for Uncertain Switched Nonlinear Systems , 2008 .

[36]  Y. Kim,et al.  L/sub 2/ gain analysis for switched systems with continuous-time and discrete-time subsystems , 2004, SICE 2004 Annual Conference.

[37]  A. Morse,et al.  STABILITY OF SWITCHED SYSTEMS WITH AVERAGE , 1999 .