A Reset-Time Dependent Approach for Stability Analysis of Nonlinear Reset Control Systems

A reset mechanism in controller can affect the stability property of a closed loop control system. In a simple word, there are stable reset control systems with unstable base-systems and also unstable reset systems with stable base-systems. The Lyapunov stability theory is a strong tool to investigate the stability of a nonlinear system. In this paper, based on the well-known Lyapunov stability concept, some stability conditions for nonlinear reset control systems are addressed. These conditions are dependent on the reset-times and hence the reset-time intervals are explicitly emerged in the stability conditions. Some applications of these results are used in numerical examples to show the effectiveness of the proposed approach.

[1]  A. Banos,et al.  Reset times-dependent stability of reset control with unstable base systems , 2007, 2007 IEEE International Symposium on Industrial Electronics.

[2]  Joaquín Carrasco,et al.  Towards ℓ2ℓ2-stability of discrete-time reset control systems via dissipativity theory , 2013, Syst. Control. Lett..

[3]  Luca Zaccarian,et al.  Stability and Performance of SISO Control Systems With First-Order Reset Elements , 2011, IEEE Transactions on Automatic Control.

[4]  Luca Zaccarian,et al.  Reset passivation of nonlinear controllers via a suitable time-regular reset map , 2011, Autom..

[5]  Orhan Beker,et al.  Submitted to IEEE Transactions on Automatic Control Plant with Integrator: An Example of Reset Control Overcoming Limitations of Linear Feedback , 2001 .

[6]  Eduardo Sontag.  A universal construction of Artstein's theorem on nonlinear stabilization , 1989 .

[7]  Alfonso Baños,et al.  Reset times-dependent stability of reset control systems , 2007, 2007 European Control Conference (ECC).

[8]  Guoliang Yang,et al.  Less Conservative Stability Criteria for Discrete‐Time Nonlinear Stochastic Singular Systems with Mixed Time‐Delay , 2013 .

[9]  Luca Zaccarian,et al.  Analytical and numerical Lyapunov functions for SISO linear control systems with first‐order reset elements , 2011 .

[10]  Wei Xing Zheng,et al.  Input-to-state stability for networked control systems via an improved impulsive system approach , 2011, Autom..

[11]  Liu Feng,et al.  Stability condition for sampled data based control of linear continuous switched systems , 2011, Syst. Control. Lett..

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

[13]  Arjan van der Schaft,et al.  A passivity-based approach to reset control systems stability , 2010, Syst. Control. Lett..

[14]  Alfonso Baños,et al.  Well-Posedness of Reset Control Systems as State-Dependent Impulsive Dynamical Systems , 2012 .

[15]  Defeng He,et al.  Input‐to‐state stability of min‐max MPC scheme for nonlinear time‐varying delay systems , 2012 .

[16]  Jian Xiao,et al.  Stability analysis and control synthesis of switched impulsive systems , 2012 .

[17]  Jun Zhao,et al.  Stability Properties of Switched Nonlinear Delay Systems with Synchronous or Asynchronous Switching , 2015 .

[18]  Alireza Khayatian,et al.  Reset law design based on robust model predictive strategy for uncertain systems , 2014 .

[19]  Alfonso Baños,et al.  Reset control systems with reset band: Well-posedness, limit cycles and stability analysis , 2014, Syst. Control. Lett..

[20]  Lihua Xie,et al.  Stability analysis and design of reset control systems with discrete-time triggering conditions , 2012, Autom..

[21]  M Maarten Steinbuch,et al.  Performance analysis of reset control systems , 2010 .

[22]  C. Cai,et al.  LMI‐based stability analysis of linear hybrid systems with application to switched control of a refrigeration process , 2012 .

[23]  Luca Zaccarian,et al.  Stability properties of reset systems , 2008, Autom..

[24]  Youyi Wang,et al.  Stability analysis and design of reset systems: Theory and an application , 2009, Autom..

[25]  J. Daafouz,et al.  Stabilization of linear impulsive systems through a nearly-periodic reset , 2013 .

[26]  Orhan Beker,et al.  Fundamental properties of reset control systems , 2004, Autom..