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In this paper we extend the finite-time stability (FTS) theory to two dimensional (2D)-systems. Such class of systems plays an important role in many engineering contexts, such as digital filtering, image processing, gas absorpsion technology, as well as in other fields, like seismological data processing, thermal and industrial processes. Each independent variable of a 2D-systems attains values into...
In this paper we investigate the annular finite-time stability (AFTS) problem for linear systems. A system is said to be annular finite-time stable if the norm of the system state remains within an upper and lower treshold for a given finite interval of time. Two necessary and sufficient conditions are provided for AFTS, the former requiring the solution of a differential Lyapunov equation (DLE),...
In this paper we deal with the finite-time stability problem for quadratic systems. Such class of systems plays an important role in the modeling of a wide class of nonlinear processes (electrical, robotic, biological, etc.). The main results of the paper consist of two sufficient conditions for finite-time stability analysis and finite-time stabilization via static state feedback; both conditions...
In this paper the problem of input-output finite-time stability (IO-FTS) and stabilization of linear time-varying systems is dealt with. The classical definition of IO-FTS is extended to that one of structured IO-FTS, since this allows to incorporate, in the definition of the stabilization problem, some amplitude constraints on the control input variables. A necessary and sufficient condition and...
The problem of input-output finite-time stabilization of linear time-varying systems via dynamic output feedback is tackled in this paper. Sufficient conditions are provided in terms of Differential Linear Matrix Inequalities feasibility problems, which can be solved numerically in an efficient way by using off-the-shelf optimization tools, as illustrated by the proposed examples.
In the recent paper [3] a sufficient condition for Input-Output Finite-Time stability (IO-FTS) has been provided by the authors. By using an approach based on Reachability Gramian theory, in this paper we show that such condition, which requires the solution of a feasibility problem involving differential linear matrix inequalities (DLMIs), is also necessary for IO-FTS when the class of system inputs...
In this paper we study the robustness analysis problem for linear continuous-time systems subject to parametric time-varying uncertainties making use of piecewise linear (polyhedral) Lyapunov functions. A given class of Lyapunov functions is said to be ldquouniversalrdquo for the uncertain system under consideration if the search of a Lyapunov function that proves the robust stability of the system...
When only the input-output behavior of a dynamical system is of concern, usually Bounded-Input Bounded-Output (BIBO) stability is studied, for which several results exist in literature. The present paper investigates the analogous concept in the framework of Finite Time Stability (FTS), namely the Input-Output FTS. A system is said to be IO finite time stable if, assigned a bounded input class and...
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