New results on switched linear systems with actuator saturation

This paper further studies the analysis and control problems of continuous-time switched linear systems subject to actuator saturation. Using the norm-bounded differential inclusion description of the saturated systems and the minimal switching rule, a set of switched output feedback controllers is designed to minimise the disturbance attenuation level defined by the regional gain over a class of energy-bounded disturbances. The synthesis conditions are expressed as bilinear matrix inequalities, and can be solved by numerical search coupled with linear matrix inequality optimisation. Compared to the previous method based on polytopic differential inclusion, the proposed approach has good scalability and potentially renders better performance. Numerical examples are provided to verify the effectiveness of the proposed approach.

[1]  Jun Zhao,et al.  On stability, L2-gain and Hinfinity control for switched systems , 2008, Autom..

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

[3]  Yang Tang,et al.  Exponential Synchronization of Coupled Switched Neural Networks With Mode-Dependent Impulsive Effects , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[4]  Franco Blanchini,et al.  A separation principle for linear switching systems and parametrization of all stabilizing controllers , 2008, 2008 47th IEEE Conference on Decision and Control.

[5]  R. Decarlo,et al.  Perspectives and results on the stability and stabilizability of hybrid systems , 2000, Proceedings of the IEEE.

[6]  D. Bernstein,et al.  A chronological bibliography on saturating actuators , 1995 .

[7]  Jamal Daafouz,et al.  Suboptimal Switching Control Consistency Analysis for Switched Linear Systems , 2013, IEEE Transactions on Automatic Control.

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

[9]  Ligang Wu,et al.  Fault detection of discrete-time switched systems with distributed delays: input–output approach , 2013, Int. J. Syst. Sci..

[10]  Zongli Lin,et al.  Disturbance attenuation by output feedback for linear systems subject to actuator saturation , 2009 .

[11]  Asier Ibeas,et al.  On the Global Asymptotic Stability of Switched Linear Time-Varying Systems with Constant Point Delays , 2008 .

[12]  Dongmei Chen,et al.  Closed Loop Stability of Switching Controller for Wind Turbine , 2011 .

[13]  N.H. McClamroch,et al.  Performance benefits of hybrid control design for linear and nonlinear systems , 2000, Proceedings of the IEEE.

[14]  R. Decarlo,et al.  Construction of piecewise Lyapunov functions for stabilizing switched systems , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[15]  Franco Blanchini,et al.  A Separation Principle for Linear Switching Systems and Parametrization of All Stabilizing Controllers , 2008, IEEE Transactions on Automatic Control.

[16]  Zongli Lin,et al.  Output Feedback Stabilization of Linear Systems With Actuator Saturation , 2007, IEEE Transactions on Automatic Control.

[17]  Jamal Daafouz,et al.  Dynamic output feedback Hinfinity control of switched linear systems , 2011, Autom..

[18]  S. Tarbouriech,et al.  Control design for linear systems with saturating actuators and /spl Lscr//sub 2/-bounded disturbances , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[19]  Fen Wu,et al.  Output-feedback control for switched linear systems subject to actuator saturation , 2012, Int. J. Control.

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

[21]  Jianghai Hu,et al.  Infinite-Horizon Switched LQR Problems in Discrete Time: A Suboptimal Algorithm With Performance Analysis , 2012, IEEE Transactions on Automatic Control.

[22]  R. Decarlo,et al.  Asymptotic Stability of m-Switched Systems using Lyapunov-Like Functions , 1991, 1991 American Control Conference.

[23]  M. De La Sen,et al.  Stable multi-estimation model for single-input single-output discrete adaptive control systems , 2004 .

[24]  Zongli Lin,et al.  Low gain feedback , 1999 .

[25]  Sophie Tarbouriech,et al.  Control of Uncertain Systems with Bounded Inputs , 1997 .

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

[27]  Gérard Scorletti,et al.  Output Feedback Control with Input Saturations: LMI Design Approaches , 2001, Eur. J. Control.

[28]  Tingshu Hu,et al.  Control Systems with Actuator Saturation: Analysis and Design , 2001 .

[29]  A. Michel,et al.  Stability theory for hybrid dynamical systems , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[30]  Luca Zaccarian,et al.  Stability and Performance for Saturated Systems via Quadratic and Nonquadratic Lyapunov Functions , 2006, IEEE Transactions on Automatic Control.

[31]  Tingshu Hu,et al.  Control Systems with Actuator Saturation: Analysis and Design , 2001 .

[32]  Anders Rantzer,et al.  Piecewise linear quadratic optimal control , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[33]  Faryar Jabbari,et al.  Disturbance attenuation for systems with input saturation: An LMI approach , 1999, IEEE Trans. Autom. Control..

[34]  M. Morari,et al.  Model Predictive Control in Power Electronics: A Hybrid Systems Approach , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[35]  A. Teel,et al.  Stability and performance for saturated systems via quadratic and non-quadratic Lyapunov functions ∗ , 2022 .

[36]  João Pedro Hespanha,et al.  Hybrid Modeling of TCP Congestion Control , 2001, HSCC.

[37]  Fen Wu,et al.  Analysis and control of switched linear systems via modified Lyapunov–Metzler inequalities , 2014 .

[38]  A. Morse,et al.  Basic problems in stability and design of switched systems , 1999 .

[39]  Huijun Gao,et al.  Distributed Synchronization in Networks of Agent Systems With Nonlinearities and Random Switchings , 2013, IEEE Transactions on Cybernetics.

[40]  Tingshu Hu,et al.  Output regulation of linear systems with bounded continuous feedback , 2004, IEEE Transactions on Automatic Control.

[41]  Luca Zaccarian,et al.  Output feedback design for saturated linear plants using deadzone loops , 2009, Autom..

[42]  Wenbing Zhang,et al.  Exponential synchronization of coupled switched neural networks with mode-dependent impulsive effects. , 2013, IEEE transactions on neural networks and learning systems.