Dwell-Time-Based Standard $H_\infty$ Control of Switched Systems Without Requiring Internal Stability of Subsystems

This paper investigates standard <inline-formula><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> control of switched systems via dwell-time switchings without posing any internal stability requirements on subsystems of the switched systems. First, a sufficient condition is formed by specifying lower and upper bounds of the dwell time, constraining upper bound of derivative of a Lyapunov function of the active subsystem, and forcing the Lyapunov function values of the overall switched system to decrease at switching times to achieve standard <inline-formula><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> control of unforced switched linear systems. Then, in the same framework of the dwell time, sufficient conditions are given for that of the corresponding forced switched linear systems by further designing state feedback controllers. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed results.

[1]  Tian You Chai.  An indirect stochastic adaptive scheme with on-line choice of weighting polynomials , 1990 .

[2]  Fang Deng,et al.  Wearable Thermoelectric Power Generators Combined With Flexible Supercapacitor for Low-Power Human Diagnosis Devices , 2017, IEEE Transactions on Industrial Electronics.

[3]  Wu-Hua Chen,et al.  Functional observers for linear impulsive systems , 2011, CCC 2011.

[4]  Weiyao Lan,et al.  Explicit Construction of H Control Law for a Class of Nonminimum Phase Nonlinear Systems , 2007, 2007 American Control Conference.

[5]  Wu-Hua Chen,et al.  Impulsive functional observers for linear systems , 2011 .

[6]  Bart De Schutter,et al.  Stabilization and robust H⃵ control for sector-bounded switched nonlinear systems , 2014, Autom..

[7]  M. Branicky.  Multiple Lyapunov functions and other analysis tools for switched and hybrid systems , 1998, IEEE Trans. Autom. Control..

[8]  Patrizio Colaneri,et al.  H∞ and Dwell Time Specifications of Continuous-Time Switched Linear Systems , 2010 .

[9]  Corentin Briat,et al.  Affine Characterizations of Minimal and Mode-Dependent Dwell-Times for Uncertain Linear Switched Systems , 2012, IEEE Transactions on Automatic Control.

[10]  Jian Xiao,et al.  Stabilization of switched continuous-time systems with all modes unstable via dwell time switching , 2014, Autom..

[11]  Jun Zhao,et al.  On stability, L 2 -gain and H 8 control for switched systems , 2008 .

[12]  Franco Blanchini,et al.  Convexity of the cost functional in an optimal control problem for a class of positive switched systems , 2014, Autom..

[13]  Corentin Briat,et al.  Convex lifted conditions for robust l2-stability analysis and l2-stabilization of linear discrete-time switched systems with minimum dwell-time constraint , 2014, Autom..

[14]  Wei Xing Zheng,et al.  Delay-Independent Minimum Dwell Time for Exponential Stability of Uncertain Switched Delay Systems , 2010, IEEE Transactions on Automatic Control.

[15]  Joao P. Hespanha,et al.  Logic-based switching algorithms in control , 1998 .

[16]  P. Khargonekar,et al.  Robust stabilization of uncertain linear systems: quadratic stabilizability and H/sup infinity / control theory , 1990 .

[17]  Truong Q. Nguyen,et al.  Robust and reduced-order filtering: new LMI-based characterizations and methods , 2001, IEEE Trans. Signal Process..

[18]  Jun Fu,et al.  Local optimization of dynamic programs with guaranteed satisfaction of path constraints , 2015, Autom..

[19]  Jun Fu,et al.  Global finite-time stabilization of a class of switched nonlinear systems with the powers of positive odd rational numbers , 2015, Autom..

[20]  Hiroyuki Kawai,et al.  Passivity-Based Dynamic Visual Feedback Control for Three-Dimensional Target Tracking: Stability and $L_{2}$-Gain Performance Analysis , 2007, IEEE Transactions on Control Systems Technology.

[21]  Wu-Hua Chen,et al.  Impulsive observers with variable update intervals for Lipschitz nonlinear time-delay systems , 2013, Int. J. Syst. Sci..

[22]  Corentin Briat,et al.  Stability analysis and stabilization of stochastic linear impulsive, switched and sampled-data systems under dwell-time constraints , 2016, Autom..

[23]  Fen Wu,et al.  Analysis and control of switched linear systems via dwell-time min-switching , 2014, Syst. Control. Lett..

[24]  Jun Zhao,et al.  Stability and L2-gain analysis for switched delay systems: A delay-dependent method , 2006, Autom..

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

[26]  Corentin Briat,et al.  Convex conditions for robust stabilization of uncertain switched systems with guaranteed minimum and mode-dependent dwell-time , 2015, Syst. Control. Lett..

[27]  Uri Shaked,et al.  Robust stability and stabilization of linear switched systems with dwell time , 2010, 2010 Conference on Control and Fault-Tolerant Systems (SysTol).

[28]  Ben M. Chen,et al.  Explicit construction of Hinfinity control law for a class of nonminimum phase nonlinear systems , 2008, Autom..

[29]  Jun Zhao,et al.  On Finite-Time Stability of Cyclic Switched Nonlinear Systems , 2015, IEEE Transactions on Automatic Control.

[30]  Guo-Ping Liu,et al.  $L_{2}$ -Gain of Systems With Input Delays and Controller Temporary Failure: Zero-Order Hold Model , 2011, IEEE Transactions on Control Systems Technology.

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

[32]  Vladimir L. Kharitonov,et al.  Stability of Time-Delay Systems , 2003, Control Engineering.

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

[34]  Suat Gumussoy,et al.  Sensitivity Minimization by Strongly Stabilizing Controllers for a Class of Unstable Time-Delay Systems , 2009, IEEE Transactions on Automatic Control.

[35]  Tianyou Chai,et al.  Dwell-Time-Based Observer Design for Unknown Input Switched Linear Systems Without Requiring Strong Detectability of Subsystems , 2017, IEEE Transactions on Automatic Control.

[36]  J.C. Geromel,et al.  ${\cal H}_\infty$ and Dwell Time Specifications of Continuous-Time Switched Linear Systems , 2010, IEEE Transactions on Automatic Control.

[37]  Peng Shi,et al.  Non-weighted quasi-time-dependent H∞ filtering for switched linear systems with persistent dwell-time , 2015, Autom..

[38]  Chengzhi Yuan,et al.  Hybrid Control for Switched Linear Systems With Average Dwell Time , 2015, IEEE Transactions on Automatic Control.

[39]  Jun Zhao,et al.  Backstepping design for global stabilization of switched nonlinear systems in lower triangular form under arbitrary switchings , 2010, Autom..

[40]  Hai Lin,et al.  Switched Linear Systems: Control and Design , 2006, IEEE Transactions on Automatic Control.

[41]  Shuzhi Sam Ge,et al.  Switched Linear Systems , 2005 .

[42]  Wei Lin,et al.  Almost disturbance decoupling for a class of high-order nonlinear systems , 2000, IEEE Trans. Autom. Control..

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

[44]  Jun Zhao,et al.  $H_{\infty}$ Control of Switched Nonlinear Systems in $p$-Normal Form Using Multiple Lyapunov Functions , 2012, IEEE Transactions on Automatic Control.

[45]  Patrizio Colaneri,et al.  Stability and Stabilization of Continuous-Time Switched Linear Systems , 2006, SIAM J. Control. Optim..

[46]  Hao Liu,et al.  Weighted H ∞ performance analysis of switched linear systems with mode-dependent average dwell time , 2013, Int. J. Syst. Sci..

[47]  Uri Shaked,et al.  Robust State-Dependent Switching of Linear Systems With Dwell Time , 2013, IEEE Transactions on Automatic Control.

[48]  Dong Yue,et al.  Network-based robust H ∞ control of systemswith uncertainty , 2005 .