State-Dependent Switching $\mathcal{L}_{2}$ Gain for Analyzing the Fluctuations in Transient Responses After a System Switch

We propose a state-dependent switching $\mathcal{L}_{2}$ gain for analyzing the fluctuations in transient response after an unpredictable switch between two linear time-invariant systems. Its value depends on the state of a pre-switch system at a switching time. Thus, it enables us to theoretically discuss the effects of the situation at a switching time on the fluctuations in transient responses after the switch. For example, its value distribution in the state space of a pre-switch system can be used for evaluating the dangerous extent of the situation at an occurrence time of a control device failure.

[1]  Toru Asai.  Necessary and Sufficient Conditions for Analysis of L2 Gain across Switching , 2005 .

[2]  Noboru Sebe,et al.  New switching L2 gain analysis for a restart with controller resets after maintenance , 2015 .

[3]  Patrizio Colaneri.  Dwell time analysis of deterministic and stochastic switched systems , 2009, 2009 European Control Conference (ECC).

[4]  Patrizio Colaneri,et al.  Homogeneous Rational Lyapunov Functions for Performance Analysis of Switched Systems With Arbitrary Switching and Dwell Time Constraints , 2017, IEEE Transactions on Automatic Control.

[5]  Patrizio Colaneri,et al.  A Nonconservative LMI Condition for Stability of Switched Systems With Guaranteed Dwell Time , 2012, IEEE Transactions on Automatic Control.

[6]  Kenji Hirata,et al.  ℒ2-induced gains of switched systems and classes of switching signals , 2010, 49th IEEE Conference on Decision and Control (CDC).

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

[8]  Noboru Sebe,et al.  Controller Reset Strategy for Anti‐Windup Based on Switching L2 Gain Analysis , 2017 .

[9]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[10]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[11]  Noboru Sebe,et al.  Probabilistic safety management of control laws against deviations from normal operating-range , 2010, 2010 Conference on Control and Fault-Tolerant Systems (SysTol).

[12]  Noboru Sebe,et al.  Switching ℒ2 gain for evaluating the fluctuations in transient responses after an unpredictable system switch , 2019, Int. J. Control.

[13]  Toru Asai.  LMI-based synthesis for robust attenuation of disturbance responses due to switching , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[14]  João Pedro Hespanha,et al.  Root-mean-square gains of switched linear systems , 2003, IEEE Trans. Autom. Control..

[15]  Noboru Sebe,et al.  ℒ︁2 gain analysis of linear systems with a single switching , 2011 .

[16]  Toru Asai,et al.  Analysis of the worst-case bumpy responses based on LMIs , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..