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3) Example 3: Consider now the time-varying system The solution with dynamic matrix and solution given respectively by [15, p. 149] A(t) = 0 1 1 + t ; x(t; t 0 ; x 0) = 1 + t0 1 + t x 0 and thus the system is asymptotically stable but not uniformly asymp-totically stable. In fact, Theorem 4 provides X(t) = (1 + t 0) 2 (1 + t) 2 as the solution of (4) and,(More)
A b s t r a c t In this paper we consider the Finite-Time Stability and Finite-time Boundedness problems for linear systems subject to exogenous disturbances. The main results of the paper are some necessary and sufficient conditions, obtained by means of an approach based on operator theory; such conditions improve some recent results on this topic. An(More)
In this paper the problem of input-output finite-time stabilization of linear time-varying systems is dealt with. The classical definition of input-output finite-time stability (IO-FTS) is extended to that one of structured IO-FTS, which allows to incorporate, in the definition of the stabilization problem, some amplitude constraints on the control input(More)
— This paper deals with the finite-time stability problem for a special class of hybrid systems, namely impulsive dynamical linear systems (IDLS). IDLS are systems that exhibit jumps in the state trajectory. Both analysis and design problems are tackled, both for time-dependent and state-dependent IDLS. The presented results require to solve feasibility(More)