The finite-time stability of Caputo fractional order time-lagged switching linear systems are investigated to better understand the effect of systematic time-lagged on the stability of fractional order switching systems.Firstly,by solving the given fractional order time-lagged linear system,the inequality condition satisfied by the Caputo fractional order derivative of Lyapunov function along the fractional order linear time-lagged system is derived.Secondly,based on this inequality condition and the properties of the Heaviside step function,the equivalent solution of the segmentally defined differential function with Caputo fractional order derivatives is obtained;by means of the derived lemma,a sufficient condition for the finite-time stability of the fractional order time-lagged linear switching system is obtained.Finally,the validity of the proposed method is verffied by two arithmetic examples.By utilizing the Heaviside step function,the obtained equivalent solutions of segmentally defined fractional order calculus inequalities effectively overcome the memory defects of neglecting fractional order operators in the existing study of the stability problems of fractional order switching time-lagged systems.
Fractional order calculus/Switching linear system/Time-lagged/Caputo fractional order/Finite-time stability/Lyapunov function/Segmentally defined differential function
维普
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