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Health Technology Assessment (HTA) and Six Sigma (SS) have largely proved their reliability in the healthcare context. The former focuses on the assessment of health technologies to be introduced in a healthcare system. The latter deals with the improvement of the quality of services, reducing errors and variability in the healthcare processes. Both the approaches demand a detailed analysis, evidence-based decisions, and efficient control plans. In this paper, the SS is applied as a support tool for HTA of two antibiotics with the final aim of assessing their clinical and organizational impact in terms of postoperative Length Of Stay (LOS) for patients undergoing tongue cancer surgery. More specifically, the SS has been implemented through its main tool, namely the DMAIC (Define, Measure, Analyse, Improve, Control) cycle. Moreover, within the DMAIC cycle, a modelling approach based on a multiple linear regression analysis technique is introduced, in the Control phase, to add complementary information and confirm the results obtained by the statistical analysis performed within the other phases of the SS DMAIC. The obtained results show that the proposed methodology is effective to determine the clinical and organizational impact of each of the examined antibiotics, when LOS is taken as a measure of performance, and guide the decision-making process. Furthermore, our study provides a systematic procedure which, properly combining different and well-assessed tools available in the literature, demonstrated to be a useful guidance for choosing the right treatment based on the available data in the specific circumstance.

We consider the tracking problem for a robotic manipulator. First, we propose an approach which allows one to place the problem of designing an optimal control law for a rigid manipulator in the context of linear matrix inequalities (LMIs) optimization; this permits one to include in the synthesis of the control law and constraints concerning the control amplitude. Then we consider flexible links manipulators, showing how the synthesis of the controller has to be modified in order to obtain good performances in presence of flexible elements.

In this paper, we investigate some finite-time control problems for stochastic linear time-varying systems, described by an Itô type differential equation. In particular, the annular stochastic finite-time stability control problem is dealt with. In this context, it is required that the norm of the state variables remains bounded between an inner and an outer ellipsoid, during a finite-interval of time. The first contribution of the paper consists of two sufficient conditions for stability, which are derived by exploiting an approach based on time-varying quadratic Lyapunov functions. The first condition requires the solution of two generalised differential Lyapunov equations; the latter the existence of a feasible solution to a pair of differential linear matrix inequalities. As particular cases, we obtain sufficient conditions for stochastic finite-time stability (in this last case, the lower ellipsoid collapses to the origin). From the analysis conditions, a sufficient condition is derived for the annular stochastic finite-time stabilisation via both state and output feedback. Some numerical examples illustrate the application of the proposed methodology and show that our approach attains less conservative results than those obtainable with the existing literature. Moreover, an application of the annular stochastic finite-time stability approach to the stabilisation problem of a satellite with respect to the geomagnetic field is presented.

Foetal heart rate (FHR) variability is known to be a very important feature in the diagnosis of foetal well-being. Despite its clinical importance and the widespread use of foetal monitoring, a standard definition of FHR variability (FHRV) and an agreement concerning the methodologies to be employed in its evaluation are still lacking. Often, FHRV is computed in tracts of FHR signals in which both accelerations and decelerations are absent, thus making it very difficult to assess it for signals with several and closely spaced events of this kind. In this work, we propose an automated method for estimating the FHRV signal, defining it as the difference between the FHR signal and the floatingline, where the latter is the imaginary line that follows accelerations and decelerations, taking into account the frequency characteristics of these events. We tested the software developed for this purpose on both simulated and real FHR signals (sets of 50 signals). In the case of simulated signals, the average value of the mean square error vector between the simulated floatingline and that estimated was only 0.04 bpm 2 . In the case of real signals, however, in absence of a reference gold standard, the estimated floatinglines were visually assessed by a team of five expert obstetricians who judged them matching to the definition in 96% of cases. As regards the evaluation of FHRV, using the simulated FHR signals, we compared the estimated values with the reference values of short term variability (STV) and sympathovagal balance (SVB), two very significant parameters employed in computerised foetal monitoring, and obtained an error lower than 1.5% for the STV index, and an underestimation of the SVB index with an error of about 4.5%. Finally, we compared the proposed method for the estimation of the floatingline with more traditional filters (moving average and FIR with Hamming window) which showed, on average, a worse performance (quantified by mean square errors up to five times higher).

This paper deals with the finite-time boundedness (FTB) of linear time-varying (LTV) systems; in this context, the novel contribution of our work goes in several directions. The first result is a sufficient condition for FTB when the plant input is generated by an exo-system; it is worth noting that constant, norm bounded signals, which most part of the previous literature has considered so far, belong to such class of inputs. To this regard, it is possible to compare our result with the existing literature, which shows that our approach yields less conservative conditions. The second result provided in the paper, is a sufficient condition for FTB when the input belongs to L 2 , the class of square integrable signals, which have never been considered so far. In both cases, the proposed results require the solution of a feasibility problem constrained by differential linear matrix inequalities (DLMIs). A third contribution of the paper proves that, from the system-theoretic point of view, the obtained FTB conditions can be interpreted in terms of the norm of a suitable input–output operator. As a consequence of this fact, we are able to find alternative and equivalent conditions for FTB, both for the exogenous and the L 2 cases, which are based on the solution of differential Lyapunov equations (DLEs), which are much more efficient from the computational point of view. The DLMI-based condition, however, is fundamental to solve the design problem, which is also investigated in the paper. Some examples show that the proposed technique is less conservative with respect to the previous literature, when exogenous inputs are considered, and its effectiveness when L 2 signals are considered. Moreover, one example is devoted to show that the analysis approach, based on the solution of DLE, is much more efficient from the computational point of view with respect to the one based on DLMIs; finally the last example investigates the application of the state feedback control technique.

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 Amato et al. (2011), 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.

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.

International audience; In this note, we deal with linear systems and we extend to the finite-time setting the concepts of stabilizability and detectability. It will be shown that, similarly to what happens in the classical Lyapunov framework, even in the finite-time context, stabilizability and detectability play a role into the existence of stabilizing dynamical controllers. We prove that a dynamic output feedback controller, which finite-time stabilizes the overall closed-loop system, exists if and only if the open-loop system is finite-time detectable and stabilizable plus a further linear matrix inequality coupling condition. We also show that, in the finite-time context, the equivalence between stabilizability via output feedback and stabilizability via observer-based controllers is no longer true.

In this study, the problem of input–output finite-time stabilisation 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 stabilisation problem, some amplitude constraints on the control input variables. A sufficient condition and a necessary and sufficient condition for structured IO finite-time stabilisation are provided in the case of L ∞ and L 2 inputs, respectively. Such conditions require the existence of a solution to a certain differential linear matrix inequality. The theory is applied to design the active suspension control system for a two-degree-of-freedom quarter-car model.

Sufficient conditions for the finite-time stability (FTS) of impulsive dynamical linear systems (IDLSs) have been provided in Amato, Ambrosino, Cosentino, and De Tommasi (2011). In this brief note we show that, when time-dependent IDLSs are dealt with, the sufficient condition for FTS derived in Amato, Ambrosino, Cosentino et al. (2011) is also necessary. Moreover, an alternative necessary and sufficient condition for FTS is proposed, which is based on the solution of a coupled differential-difference Lyapunov equation. This condition turns out to be more efficient from the computational point of view. The proposed approach is illustrated through some examples.

This study addresses the problem of designing a guaranteed cost controller for non-linear discrete quadratic systems. More specifically, the main contribution concerns a sufficient condition for the existence of a state-feedback controller achieving a certain guaranteed cost, whenever the state trajectories start from a prescribed set of initial conditions. The controller design requires the solution of a convex optimisation problem involving linear matrix inequalities, which can be efficiently solved via available optimisation algorithms. Finally, the proposed design methodology is illustrated via an example concerning the attitude control of an unmanned aerial vehicle.

In this paper, the first of two companion works, we deal with linear systems and extend to the finite-time setting the concepts of stabilizability and detectability. After stating necessary and sufficient conditions for finite-time stabilizability (FT-stab) and detectability (FT-det), in terms of feasibility conditions constrained by differential linear matrix inequalities (DLMIs), we investigate the relationships between the existence of dynamical output feedback finite-time stabilizing controllers and the concepts of FT-stab and FT-det. In the classical Lya-punov framework, a consequence of the well known Separation Principle is that stabilizability via dynamic output feedback controllers is equivalent to stabilizability (via state feedback) plus detectablity. In this paper, we show that, even in the finite-time context, stabilizability and detectability play a role into the existence of stabilizing dynamical controllers, although with some differences. Indeed we prove that a dynamic output feedback controller which finite-time stabilizes the overall closed loop system exists if and only if the open loop system is finite-time detectable and stabilizable plus a further LMI condition. Based on this result, a procedure for the design of a suitable output feedback controller is provided; such procedure requires the solution of some optimization problems constrained by DLMIs. A numerical example illustrates the benefits of the proposed approach.

In this paper and the companion work [10], we deal with linear systems and investigate the concepts of stabilizability and detectability in the finite-time context. Here, our aim is to study the relationships between the existence of observer based output feedback finite-time stabilizing controllers and the concepts of finite-time stabilizability (FT-stab) and detectability (FT-det). In the classical Lyapunov context, the Separation Principle states that stabilizability and detectability of the given linear system are necessary and sufficient for the existence of an output feedback dynamical controller which, without loss of generality, can be given a controller-observer structure. We show that this is no longer true in the finite-time context; therefore, we provide a further sufficient condition for the existence of an observer-based output feedback controller which finite-time stabilizes the closed loop system. Based on this result, a procedure for the design of a suitable controller is provided; such procedure requires the solution of some optimization problems constrained by DLMIs. A numerical example illustrates the benefits of the proposed approach.

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), the latter involving an optimization feasibility problem constrained by differential linear matrix inequalities (DLMIs). We show that the DLE-based condition is more efficient from the computational point of view; however the DLMI-based condition is the starting point to investigate the design problem. To this regard a necessary and sufficient condition for the existence of a state feedback controller which renders the closed loop annular finite-time stable is provided. A numerical example illustrates the improvement of the proposed approach with respect to those existing literature.

In the recent paper “Input-output finite-time stabilization of linear systems,” (F. Amato et al.) a sufficient condition for input–output finite-time stability (IO-FTS), when the inputs of the system are signals, has been provided; such condition requires the existence of a feasible solution to an optimization problem involving a certain differential linear matrix inequality (DLMI). Roughly speaking, a system is said to be input–output finite-time stable if, given a class of norm bounded input signals over a specified time interval of length , the outputs of the system do not exceed an assigned threshold during such time interval. IO-FTS constraints permit to specify quantitative bounds on the controlled variables to be fulfilled during the transient response. In this context, this paper presents several novel contributions. First, by using an approach based on the reachability Gramian theory, we show that the main theorem of F. Amato et al. is actually also a necessary condition for IO-FTS; at the same time we provide an alternative—still necessary and sufficient—condition for IO-FTS, in this case based on the existence of a suitable solution to a differential Lyapunov equality (DLE). We show that the last condition is computationally more efficient; however, the formulation via DLMI allows to solve the problem of the IO finite-time stabilization via output feedback. The effectiveness and computational issues of the two approaches for the analysis and the synthesis, respectively, are discussed in two examples; in particular, our methodology is used in the second example to minimize the maximum displacement and velocity of a building subject to an earthquake of given magnitude.

This is the first study of a two-part work devoted to the stability analysis and guaranteed cost control of the class of non-linear quadratic systems. For a given polytopic region in the state space, a sufficient condition is proposed to check whether an assigned region belongs to the domain of attraction of the zero equilibrium point. It is also shown that this problem is intimately related to the convergence and the computation of quadratic cost functions. Thanks to the main result of the study, both issues are casted in terms of feasibility problems involving linear matrix inequalities. A meaningful application example, involving the development of optimal strategies for integrated pest management, is illustrated at the end of this study.

The problem of the estimation of the domain of attraction for Impulsive Dynamical Systems (IDSs) is tackled in this paper. IDSs are a special class of hybrid systems that exhibit jumps in the state trajectory, which can be either time-driven (time-dependent IDSs), or driven by specific state values (state-dependent IDSs). Sufficient conditions to determine whether a polytope belongs to the domain of attraction of the zero equilibrium point are provided for both time-dependent and state-dependent IDS, when a nonlinear quadratic continuous-time dynamic is considered. The proposed results are stated in terms of Linear Matrix Inequalities problems. The effectiveness of the proposed results is shown by means of the analysis of a biological model for tumor progression.

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.

In this article, the authors 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 ‘universal’ for the uncertain system under consideration if the search of a Lyapunov function that proves the robust stability of the system can be restricted, without conservatism, to the elements of the class. In the literature, it has been shown that the class of polyhedral functions is universal, while, for instance, the class of quadratic Lyapunov functions is not. This fact justifies the effort of developing efficient algorithms for the construction of optimal polyhedral Lyapunov functions. In this context, the authors provide a novel procedure that enables to construct, in the general n-dimensional case, a polyhedral Lyapunov function to prove the robust stability of a given system. Some numerical examples are included, where the authors show the effectiveness of the proposed approach comparing it with other approaches proposed in the literature.

Robust finite-time stability (FTS) for a class of uncertain hybrid systems is tackled for the first time in this paper. In particular, uncertain impulsive dynamical linear systems (U-IDLS) are considered. U-IDLS exhibit jumps in the state trajectory that can be either time-driven (time-dependent IDLS) or driven by specific state values (state-dependent IDLS). Furthermore, U-IDLS may exhibit uncertainties both in the linear dynamic and in the jump equation. In this paper, sufficient conditions for FTS of IDLS are provided. These results require the solution of feasibility problems involving differential-difference linear matrix inequalities (D/DLMIs), which can be numerically solved in an efficient way, as illustrated in the proposed examples. Copyright © 2010 John Wiley & Sons, Ltd.

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.

The problem of the state estimation of nonlinear quadratic systems is addressed in this paper. Given an assigned polytopic region of the state space, which is enclosed into the domain of attraction of the zero equilibrium point, the main result consists of a sufficient condition for the existence of an observer which guarantees that the estimation error converges to zero, with an assigned rate, over such a prescribed region. The problem of the observer design is tackled in terms of a Linear Matrix Inequalities (LMIs) feasibility problem. Finally, the applicability of the proposed technique is discussed and illustrated through a numerical example.

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.

Quadratic systems play an important role in the modelling of a wide class of nonlinear processes (electrical, robotic, biological, etc.). For such systems, it is of mandatory importance not only to determine whether the origin of the state space is locally asymptotically stable but also to ensure that the operative range is included into the convergence region of the equilibrium. Based on this observation, this paper considers the following problem: given the zero equilibrium point of a nonlinear quadratic system, assumed to be locally asymptotically stable, and a certain polytope in the state space containing the origin, determine whether this polytope belongs to the region of attraction of the equilibrium. The proposed algorithm requires the solution of a suitable feasibility problem involving linear matrix inequalities constraints. An example illustrates the effectiveness of the proposed procedure by exploiting a population interaction model of three species.

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.

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.

In this paper we consider a linear, discrete-time system depending multi-affinely on uncertain, real time-varying parameters. A new sufficient condition for the stability of this class of systems, in terms of a feasibility problem involving linear matrix inequalities (LMIs), is obtained under the hypothesis that a bound on the rate of variation of the parameters is known. This condition, obtained by the aid of parameter dependent Lyapunov functions, obviously turns out to be less restrictive than that one obtained via the classical quadratic stability (QS) approach, which guarantees stability in presence of arbitrary time-varying parameters. An important point is that the methodology proposed in this paper may result in being less conservative than the classical QS approach even in the absence of an explicit bound on the parameters rate of variation. Concerning the synthesis context, the design of a gain scheduled compensator based on the above approach is also proposed. It is shown that, if a suitable LMI problem is feasible, the solution of such problem allows to design an output feedback gain scheduled dynamic compensator in a controller-observer form stabilizing the class of systems which is dealt with. The stability conditions are then extended to take into account L2 performance requirements. Some numerical examples are carried out to show the effectiveness and to investigate the computational burden required by the proposed approach. Copyright © 2005 John Wiley & Sons, Ltd.

This paper deals with the design of feedback strategies for a novel class of multi-player linear quadratic differential games. To this end the classical definition of Nash equilibrium solution is extended to deal with problems in which the goal of the i -th player is the tracking of a pre-specified trajectory in the state-space by adopting a state feedback control policy. In this context a sufficient condition for the existence of the optimal Nash equilibrium solution of each player is provided. Then the more general case in which the players do not know exactly the model of the game is considered; in this case each player assumes a different behaviour of the game by modelling the system dynamics by means of a linear dynamic system subject to norm bounded uncertainties. The proposed strategies guarantee to each player a given performance bound and, to be evaluated, require the solution of a set of coupled Riccati Differential Equations containing certain multiplier functions. A numerical example is provided to show the effectiveness of the proposed method.

In this paper we consider a linear time-varying system whose state equation is affected by time delays and subject to unknown, square integrable disturbances. Using a differential games approach, we provide a necessary and sufficient condition for the existence of an optimal control law minimizing the H^~ norm of the operator mapping the disturbance to the weighted control and terminal state. An example, which illustrates the proposed technique, is also provided at the end of the paper.

In this paper the robust stability problem for a linear, discrete-time uncertain system depending affinely on a vector of uncertain, time-varying parameters is considered; the novelty is that of considering bounded rate parameters. In this case the classical Quadratic Stability approach may result conservative, because it guarantees stability versus arbitrary time-varying parameters. Sufficient conditions, less conservative than those provided by the Quadratic Stability approach, are stated via an approach based on parameter dependent Lyapunov functions.

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 paper deals with the stabilization of Impulsive Dynamical Systems (IDSs) which represent a subclass of hybrid systems. The IDSs considered here are described by a continuous-time dynamics defined by a nonlinear quadratic system and exhibit discrete jumps in the state trajectory. In this paper we provide sufficient conditions for the design of both static state- and dynamical output-feedback controllers. The proposed conditions guarantee, for the closed-loop system, the local asymptotic stability of the zero equilibrium point, and the inclusion of a given polytopic region into the domain of attraction of the equilibrium itself. Specialized conditions are provided for the case of time-dependent quadratic IDSs with prescribed resetting times. The proposed results require the solution of a feasibility problem involving Linear Matrix Inequalities (LMIs), which can be efficiently solved by using off-the-shelf optimization algorithm, as shown through numerical examples.

In this paper a linear time-varying uncertain system depending in structured, norm-bounded, one-block fashion on an uncertain, real, time-varying parameter, whose magnitude is between the complex stability radius and the real stability radius, is considered. In this case, stability of the system can depend on the time rate of variation of the parameter. By utilizing parameter dependent Lyapunov functions, one can take the parameter rate of change into account and obtain sufficient conditions for stability which are less restrictive than those imposed by parameter independent Lyapunov functions.

In this paper we consider the finite-time stability (FTS) problem for linear time varying systems. In most of the previous literature, the definition of FTS exploits the standard weighted quadratic norm to define the initial and trajectory domains, which, therefore, turn out to be ellipsoidal; this is consistent with the fact that quadratic Lyapunov functions are used to derive the FTS conditions. Conversely, the recent paper [1], considers the case where the above domains are polytopic and, consequently, the analysis is performed with the aid of polyhedral Lyapunov functions. In the current work, the class of Piecewise Quadratic Lyapunov functions is considered. First, it is shown that such class of functions recovers as particular cases both quadratic and polyhedral Lyapunov functions; then a novel sufficient condition for FTS of linear time-varying systems is provided. A procedure is proposed to convert such condition into a computationally tractable problem. The examples illustrated at the end of the paper show the benefits of the proposed technique with respect to the methodologies available in the literature.

In this paper, an approach based on the concept of Finite-Time Stability is applied to the problem of designing optimal control strategies for an integrated pest management model with disease in the pest, which is subject to time-dependent impulsive control. The goal is to design a resetting law such that, given a set of admissible initial conditions, the state trajectories of the resulting impulsive quadratic system remain in a bounded region of the state space which is prescribed on the basis of some constraints on ecological balance and resource saving. The determination of an optimal resetting period, which is related to the release period of chemical pesticides, is reduced to the solution of a feasibility problem with Linear Matrix Inequalities constraints.

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 a sufficient condition for constrained IO finite-time stabilization are provided in the case of ℒ 2 and ℒ ∞ disturbance inputs, respectively. Such conditions require the existence of a feasible solution to a certain differential linear matrix inequality (DLMI). A numerical example illustrates the effectiveness of the proposed approach.

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 “universal” for the uncertain system under consideration if the robust stability of the system is equivalent to the existence of a Lyapunov function belonging to the class. In the literature it has been shown that the class of polyhedral functions is universal, while, for instance, the class of quadratic functions is not. This fact justifies the effort of developing efficient algorithms for the construction of polyhedral Lyapunov functions. In this context, we provide a low computational cost procedure, based on a novel convex condition, for the construction of a polyhedral Lyapunov function. In the section on the numerical examples, we consider some benchmark problems for the robust stability analysis and we show that the proposed low computational cost approach, though only sufficient, is less conservative than all the other approaches presented so far in the literature.

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.

This article extends the concept of input–output finite time stability (IO–FTS) to a class of hybrid systems, namely impulsive dynamical linear systems, which are systems that exhibit jumps in the state trajectory. Sufficient conditions are given for the analysis of IO–FTS and for the design of both static output and state feedback controllers, guaranteeing IO–FTS of the closed loop system. In the general case the presented results require to solve feasibility problems involving either linear matrix inequalities or bilinear matrix inequalities, which can be solved numerically in an efficient way by using off-the-shelf optimisation tools, as illustrated by the proposed examples.

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.

The concept of Input-Output Finite Time Stability (IO-FTS) is extended to time-dependent switching linear systems, which are systems with different continuous dynamics and that can exhibit state jumps driven by time. Sufficient conditions are given for the analysis of IO-FTS in the case of certain and uncertain resetting times. The presented results require to solve feasibility problems involving Difference/Differential Linear Matrix Inequalities, which can be solved numerically in an efficient way by using off-the-shelf optimization tools, as illustrated by the proposed example.

In this paper we deal with the finite-time stability analysis and control of switching linear systems, which are linear continuous-time systems with isolated discrete switching events, and whose state can undergo finite jump discontinuities. Moreover, the case in which the time occurrence of the switching events is unknown is considered. Sufficient conditions for finite-time stability and stabilization are provided in terms of feasibility problems involving differential LMIs. Numerical examples are provided to better illustrate the proposed approach.

In this paper we consider the robustness analysis problem for linear continuous-time systems subject to parametric time-varying uncertainties, making use polyhedral Lyapunov functions. In the literature it has been shown that the class of polyhedral functions is universal for the robust stability problem, while, for instance, the class of quadratic functions is not. This fact justifies the effort of developing efficient algorithms for the construction of optimal polyhedral Lyapunov functions. In this context, we provide a novel convex condition for the construction of a polyhedral Lyapunov function. Finally, to show the effectiveness of the method, we consider a numerical problem that represents a sort of benchmark for the robust stability analysis.

The present paper extends the concept of Input–Output Finite Time Stability (IO-FTS) to a class of hybrid systems, namely Impulsive Dynamical Linear Systems, which are systems that exhibit jumps in the state trajectory. Sufficient conditions are given 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 presented results require to solve feasibility problems involving Difference/Differential Linear Matrix Inequalities, which can be solved numerically in an efficient way by using off-the-shelf optimization tools, as illustrated by the proposed examples.

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.

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 are given in terms of the feasibility of a convex optimization problem, involving linear matrix inequalities. A numerical example illustrates the applicability of the proposed technique.

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.

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. Some examples illustrate the effectiveness of the proposed approach.

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 “universal” for the uncertain system under consideration if the search of a Lyapunov function that proves the robust stability of the system can be restricted, without conservatism, to the elements of the class. In the literature it has been shown that the class of polyhedral functions is universal, while, for instance, the class of quadratic Lyapunov functions is not. This fact justifies the effort of developing efficient algorithms for the construction of optimal polyhedral Lyapunov functions. In this context, we provide a novel procedure that enables to construct, in the general n-dimensional case, a polyhedral Lyapunov function to prove the robust stability of a given system. Some numerical examples are included, where we show the effectiveness of the proposed approach comparing it with other approaches proposed in the literature.