Stability, ${l}_{2}$ -Gain and Asynchronous ${H}_{{\infty}}$ Control of Discrete-Time Switched Systems With Average Dwell Time

By Lixian Zhang, Peng Shi. IEEE Transactions on Automatic Control, 2009

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H∞ control of periodic piecewise vibration systems with actuator saturation (2017, methodology): “The L2-gain performance of switched systems based on average dwell time was studied in Zhai et al. (2001), and with the average dwell time approach, asynchronous H1 control of discrete-time switched systems was studied in Zhang and Shi (2009).”
Asynchronous Filtering of Discrete-Time Switched Linear Systems With Average Dwell Time (2011, background): “Lemma 3: (Theorem 1 in [ 35 ]): Consider switched system and let and be given constants.”
Stabilization of switched continuous-time systems with all modes unstable via dwell time switching (2014, background): “…modes such as Xiang and Xiang (2009), Xiang and Xiao (2012), Xiang, Xiao, and Iqbal (2012), Zhai, Hu, Yasuda, and Michel (2000, 2001, 2002) and Zhang and Shi (2009, 2010), but it should be noted that these results also require the existence of (at least one) stable subsystem to ensure the…”
Attitude Tracking of Rigid Spacecraft With Bounded Disturbances (2011, background): “In most literature works, for unknown disturbances, control design schemes can only achieve disturbance attenuation [12]–[14].”