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Input-output finite-time stabilization of impulsive linear systems: necessary and sufficient conditions. (English) Zbl 1329.93122

Summary: The main result of this paper consists of a pair of necessary and sufficient conditions for the input-output finite-time stability of impulsive linear systems. The former requires that an optimization problem, constrained by a coupled differential/difference Linear Matrix Inequality (LMI), admits a feasible solution; the latter that the solution of a coupled differential/difference Lyapunov equation satisfies a constraint on the maximum eigenvalue. The first condition was already provided in F. Amato, G. Carannante, G. De Tommasi [”Input-output finite-time stabilisation of a class of hybrid systems via static output feedback”, Int. J. Control 84, No. 6, 1055-1066 (2011; Zbl 1245.93119)], where, however, only sufficiency was proven. The novel analysis condition (i.e. the one requiring the solution of the differential/difference Lyapunov equation) is shown to be more efficient from the computational point of view, while the result based on the differential/difference LMI is the starting point for the derivation of the design theorem. Some examples illustrate the benefits of the proposed technique.

MSC:

93D25 Input-output approaches in control theory
93C05 Linear systems in control theory
34A37 Ordinary differential equations with impulses
93B60 Eigenvalue problems

Citations:

Zbl 1245.93119
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Full Text: DOI

References:

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