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This work deals with the Input-Output Finite-Time Stability (IO-FTS) of linear discrete-time systems. In current control science, discrete-time systems play a very important role in many engineering contexts. Moreover, many discrete-time control problems are defined over a finite interval of time, therefore the development and application of finite-time control methodologies is of particular relevance. The first contribution of the paper is a pair of necessary and sufficient conditions for IO-FTS. The former involves the solution of a set of Generalized Difference Lya-punov Equations (GDLEs); the latter allows one to establish the feasibility of an optimization problem by solving a set of Difference Linear Matrix Inequalities (DLMIs). The second contribution of the paper is a theorem for IO finite-time stabilization via state feedback, followed by a more general one for stabilization via output feedback. Both conditions are necessary and sufficient, and lead to optimization problems cast in the form of DLMIs. The applicability of the devised results is illustrated through a numerical example.

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 a given (possibly finite) interval (for example, an infinite dimensional system depends on a time variable taking values in the interval [0, +∞], and on a space variable attaining values into a given finite interval). Due to the finite-interval definition of some (or all) of the independent variables, it is quite straightforward the idea to exploit, for 2D-systems, the FTS theory developed in the context of the classical one-dimensional system framework. To this regard, we provide a sufficient condition for the FTS, and a sufficient condition for the finite-time stabilization of both continuous and discrete-time linear 2D-system; such conditions will require the solution of feasibility problems based on linear matrix inequalities (LMIs). A numerical example illustrates the benefits of the proposed methodology.

The concept of Bounded-Input Bounded-Output (BIBO) stability arises when one wants to focus on the study of the the input-output behavior of a dynamical system, as opposed to the classical Lyapunov stability. 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 some boundaries in the output signal space, the output never exceeds such boundaries over a prespecified (finite) interval of time. IO-FTS has been already investigated in previous papers, whereas this is the first work dealing with the input-output behavior of an uncertain dynamical system in the FTS framework. Two sufficient conditions are given, concerning the class of 2 and ∞ input signals, for the analysis of robust IO-FTS. The applicability of the results is illustrated by means of a numerical examples.

Bounded Input Bounded Output (BIBO) stability is usually studied when only the input-output behavior of a dynamical system is of concern. The present paper investigates the analogous concept in the framework of Finite Time Stability (FTS), namely the Input-Output FTS (IO-FTS). FTS has been already investigated in several papers in terms of state boundedness, whereas in this work we deal with the characterization of the input-output behavior. Sufficient conditions are given, concerning the class of L"2 and L"~ input signals, for the analysis of IO-FTS and for the design of a static state feedback controller, guaranteeing IO-FTS of the closed-loop system. The effectiveness of the proposed results is eventually illustrated by means of some numerical examples.

The note deals with the finite-time analysis and design problems for continuous-time, time-varying linear systems. Necessary and sufficient conditions and a sufficient condition for finite-time stability are devised. Moreover, sufficient conditions for the solvability of both the state and the output feedback problems are stated. Such results require the feasibility of optimization problems involving Differential Linear Matrix Inequalities. Some numerical examples illustrate the effectiveness of the proposed approach.

This paper deals with the problem of stabilizing a bilinear system via linear state-feedback control. The proposed procedures enable us to compute a static state-feedback controller such that the zero-equilibrium point of the closed-loop system is asymptotically stable; moreover, it ensure that an assigned polytopic region is enclosed into the domain of attraction of the equilibrium point. The controller design requires the solution of a convex optimization problem involving linear matrix inequalities. The applicability of the technique is illustrated through an example, dealing with the design of a controller for a C´ uk dc–dc converter.

In this paper we investigate the stochastic finitetime stability (SFTS) problem for linear time-varying systems. The system under consideration is described by an Ito type differential equation and the Ito differentiation rule is exploited to derive conditions for SFTS. The main contribution of the paper is that we use an approach based on time-varying quadratic Lyapunov functions, which allow us to obtain less conservative conditions than the time-invariant Lyapunov functions commonly used in the literature. More specifically, we obtain a sufficient condition based on the solution of a generalized Lyapunov differential equation (GLDE) and a sufficient condition requiring the solution of a feasibility problem involving a differential LMIs (DLMI) constraint. We shall show that the DLMI based condition is less conservative and is useful to develop a sufficient condition for stochastic finite-time stabilizability via state feedback; on the other hand the GLDE condition is more efficient from the computational point of view.

This paper addresses the problem of designing a guaranteed cost controller for continuous-time nonlinear quadratic systems. The main result is a sufficient condition for the existence of a linear state feedback controller achieving an assigned guaranteed cost, whenever the state trajectories remain within a suitable invariant set. The conditions are cast in the form of Linear Matrix Inequalities (LMIs), which can be efficiently solved via available optimization algorithms. The effectiveness of the devised approach is illustrated through an example concerning the attitude control of an unmanned aerial vehicle.

This article deals with the problem of finite-time stability and stabilisation of uncertain linear systems. For linear time-varying systems subject to norm-bounded uncertainties some conditions for finite-time stability are provided. These conditions are expressed in terms of differential linear matrix inequalities. Then the problem of controller design is tackled, both for the state feedback and for the output feedback case; in both cases the controller can be found solving a suitable set of LMIs. A typical engineering case-study is included, to illustrate the applicability of the devised conditions.

In this paper we deal with some finite-time control problems for discrete-time, time-varying linear systems. First we provide necessary and sufficient conditions for finite-time stability; these conditions require either the computation of the state transition matrix of the system or the solution of a certain difference Lyapunov inequality. Then we address the design problem. The proposed conditions allow us to find output feedback controllers which stabilize the closed loop system in the finite-time sense; all these conditions can be expressed in terms of LMIs and therefore are numerically tractable, as shown in the example included in the paper.

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 some boundaries in the output signal space, the output never exceeds such boundaries over a prespecified (finite) interval of time. FTS has been already investigated in several papers in terms of state boundedness, whereas this is the first work dealing with the characterization of the input-output behavior. Sufficient conditions are given, concerning the class of L 2 and L ∞ input signals, for the analysis of IO-FTS and for the design of a static state feedback controller, guaranteeing IO-FTS of the closed loop system. Finally, the applicability of the results is illustrated by means of two numerical examples.

The finite-time stability problem for state-dependent impulsive dynamical linear systems (SD-IDLS) is addressed in this note. SD-IDLS are a special class of hybrid systems which exhibit jumps when the state trajectory reaches a resetting set. A sufficient condition for finite-time stability of SD-IDLS is provided. S-procedure arguments are exploited to obtain a formulation of this sufficient condition which is numerically tractable by means of Differential Linear Matrix Inequalities. Since such a formulation may be in general more conservative, a procedure which permits to automate its verification, without introduce conservatism, is given both for second order systems, and when the resetting set is ellipsoidal.

The problem of reverse-engineering the topology of interaction networks from time-course experimental data has received a considerable attention in the literature, due to the potential applications in the most diverse fields, comprising engineering, biology, economics and social sciences. An important insight was brought by the introduction of the concept of scale–free topology, whose implications have been widely discussed in literature over the last decade. The aim of this work is to investigate whether it is possible to improve the performances of an inference technique, based on dynamical linear systems and LMI-based optimization, by exploiting the same mechanisms that underpin scale–free networks generation, i.e. growth and preferential attachment (PA). The work is prominently concerned with applications in the biological domain, though the algorithm can be in principle adapted also to other frameworks. A statistical evaluation is performed, by using numerically simulated networks, showing that the growth and PA mechanisms actually improve the inference power of the considered technique. Finally the method is applied to a biological case-study, validating the results against experimental data available in literature.

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 problems involving Differential Linear Matrix Inequalities (DLMIs), which can be solved numerically in an efficient way, as illustrated by the proposed example.

This paper extends the finite-time stability problem to state dependent impulsive dynamical systems. For this class of hybrid systems, the state jumps when the trajectory reaches a resetting set, which is a subset of the state space. A sufficient condition for finite-time stability of state dependent impulsive dynamical systems is provided. Moreover, S-procedure arguments are exploited to obtain a formulation of this sufficient condition which is numerically tractable by means of differential linear matrix inequalities (DLMIs). Such a formulation may be in general more conservative, for this reason a procedure which allows to automate its verification, without introduce conservatism, is given both for second order systems, and when the resetting set is ellispoidal.

This paper deals with the finite-time stability problem for continuous-time linear time-varying systems with finite jumps. This class of systems arises in many practical applications and includes, as particular cases, impulsive systems and sampled-data control systems. The paper provides a necessary and sufficient condition for finite-time stability, requiring a test on the state transition matrix of the system under consideration, and a sufficient condition involving two coupled differential/difference linear matrix inequalities. The sufficient condition turns out to be more efficient from the computational point of view. Moreover, it is the starting point for solving the stabilization problem, namely for finding a state feedback controller which finite-time stabilizes the closed loop system. Some examples illustrate the effectiveness of the proposed approach.

We deal with some finite-time control problems for discrete-time linear systems. First we provide necessary and sufficient conditions for finite-time stability; these conditions require either the computation of the state transition matrix of the system or the solution of a certain difference Lyapunov equation (or inequality). The design problem, i.e. the problem of finding a state feedback controller, which stabilizes the closed loop system in the finite-time sense, is then addressed. The way these conditions can be solved numerically is finally considered.

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 example is provided to illustrate the proposed technique.

This paper deals with various finite-time analysis and design problems for continuous-time time-varying linear systems. We present some necessary and sufficient conditions for finite-time stability and then we turn to the design problem. In this context, we consider both the state feedback and the output feedback problems. For both cases, we end up with some sufficient conditions involving linear differential matrix inequalities.

This paper deals with the finite-time output feedback control problem for continuous-time, time-varying linear systems. Sufficient conditions for the existence of a controller which finite-time stabilizes the closed loop system are provided, both for the state feedback and the output feedback case. Such conditions are given in terms of a feasibility problem involving Riccati differential equations and differential linear matrix inequalities.

This paper deals with the finite time control of linear systems subject to exogenous inputs. Previous works establish sufficient conditions for finite time stabilization via state feedback in terms of LMIs based optimization. An approach to solve the more challenging output feedback problem has been recently proposed in the literature. The drawback of this last result is that the controller design is performed in two phases (static state feedback and observer) and therefore it does not exploit the possibilities offered by the design performed in one step. In this context the main result of this paper is a sufficient condition guaranteeing the finite time stabilizability via output feedback; such condition, which looks at the dynamic controller as a whole, can be converted into a feasibility problem involving LMIs. An example illustrates the proposed methodology.

In this paper we deal with some finite-time control problems for discrete-time linear systems. In particular, we consider a system subject to an exogenous output and provide a sufficient condition for finite-time boundedness, which guarantees, provided a certain Riccati difference inequality is satisfied, that the system state does not exceed some prespecified bounds. Finite-time boundedness translates into the classical concept of finite-time stability for autonomous systems. In this case necessary and sufficient conditions are proved; these conditions require either the computation of the state transition matrix of the system or the solution of a certain difference Lyapunov equation (or inequality). The design problem, i.e. the problem of finding a state feedback controller which stabilizes the closed loop system in the finite-time sense, is then addressed. The way these conditions can be solved numerically is finally considered and a design example is presented.

The problem of reverse-engineering the topology of interaction networks from time-course experimental data has received a considerable attention in the literature, due to the potential applications in the most diverse fields, comprising engineering, biology, economics and social sciences. An important insight was brought by the introduction of the concept of scale-free topology, whose implications have been widely discussed in literature over the last decade. The aim of this work is to investigate whether it is possible to improve the performances of an inference technique, based on dynamical linear systems and LMI-based optimization, by exploiting the same mechanisms that underpin scale-free networks generation, i.e. growth and preferential attachment (PA). The work is prominently concerned with applications in the biological domain, though the algorithm can be in principle adapted also to other frameworks. A statistical evaluation is performed, by using numerically simulated networks, showing that the growth and PA mechanisms actually improve the inference power of the considered technique.