In [6] a sufficient condition for the input-output finite-time stability (IO-FTS) of time-dependent impulsive dynamical linear systems has been provided in terms of a feasibility problem involving a coupled difference/differential LMI (D/DLMI). In this paper we show that such condition is also necessary; moreover an alternative necessary and sufficient condition for IO-FTS is proved. The latter condition requires the solution of a coupled difference/differential Lyapunov equation (D/DLE) and is shown to be more efficient, from the computational point of view, than the D/DLMI based condition. In order to prove the main result, we exploit the definition of controllability Gramian extended to impulsive systems. An example illustrates the benefits of the proposed technique.

Necessary and Sufficient Conditions for Input-Output Finite-Time Stability of Impulsive Dynamical Systems

F. Amato;DE TOMMASI, GIANMARIA;PIRONTI, ALFREDO
2015

Abstract

In [6] a sufficient condition for the input-output finite-time stability (IO-FTS) of time-dependent impulsive dynamical linear systems has been provided in terms of a feasibility problem involving a coupled difference/differential LMI (D/DLMI). In this paper we show that such condition is also necessary; moreover an alternative necessary and sufficient condition for IO-FTS is proved. The latter condition requires the solution of a coupled difference/differential Lyapunov equation (D/DLE) and is shown to be more efficient, from the computational point of view, than the D/DLMI based condition. In order to prove the main result, we exploit the definition of controllability Gramian extended to impulsive systems. An example illustrates the benefits of the proposed technique.
9781479986842
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11588/610255
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