Showing papers by "Francesco Amato published in 2007"

Output feedback control of nonlinear quadratic systems

Abstract: This paper provides some sufficient conditions for the stabilization of nonlinear quadratic systems via output feedback. The main contribution consists of a design procedure which enables to find a dynamic output feedback controller guaranteeing for the closed-loop system: i) the local asymptotic stability of the zero equilibrium point; ii) the inclusion of a given polytopic region into the domain of attraction of the zero equilibrium point. This design procedure is formulated in terms of a Linear Matrix Inequalities (LMIs) feasibility problem, which can be efficiently solved via available optimization algorithms. The effectiveness of the proposed methodology is shown through a numerical example.

Linear matrix inequalities approach to reconstruction of biological networks.

Abstract: The general problem of reconstructing a biological interaction network from temporal evolution data is tackled via an approach based on dynamical linear systems identification theory. A novel algorithm, based on linear matrix inequalities, is devised to infer the interaction network. This approach allows to directly taking into account, within the optimisation procedure, the a priori available knowledge of the biological system. The effectiveness of the proposed algorithm is statistically validated, by means of numerical tests, demonstrating how the a priori knowledge positively affects the reconstruction performance. A further validation is performed through an in silico biological experiment, exploiting the well-assessed cell-cycle model of fission yeast developed by Novak and Tyson.

Stabilization of bilinear systems via linear state feedback control

Abstract: In this paper we consider the problem of stabilizing a bilinear system via linear state feedback control A procedure is proposed which, given a polytope V surrounding the origin of the state space, finds, if existing, a controller in the form u = Kx, such that the zero equilibrium point of the closed loop system is asymptotically stable and V is enclosed into the domain of attraction of the equilibrium The controller design requires the solution of a convex optimization problem involving linear matrix inequalities An example illustrates the applicability of the proposed technique

A Haemodynamic Model of the Venous Network of the Lower Limbs

Abstract: The pathologies of the venous system are characterized by a relevant socioeconomic impact in western countries. To this regard, the blood flow correction allows to solve the most important venous pathologies. In these cases, in order to guarantee the restoration of normal blood flow by means of proper modifications of the venous network, the correct planning of haemodynamics surgical operations is needed; such planning in turn depends on the right analysis of the possible consequences of flow modification. To this end, a mathematical model, that allows to precisely study the physiological and pathological behaviour of the venous network of the lower limbs, has been developed. The final goal is to use this model as an instrument helpful to plan surgical operations and give guidelines for the design and the test of new artificial devices. As for the modelling processing, a lumped parameters model has been derived with a resolution which allows to take into account the anatomic characteristics of the venous system.

Finite-time stability of linear systems: an approach based on polyhedral Lyapunov functions

Abstract: In this paper we consider the finite-time stability problem for linear systems. Differently from previous papers, the stability analysis is performed with the aid of polyhedral Lyapunov functions rather than with the classical quadratic Lyapunov functions. In this way we are able to manage more realistic constraints on the state variables; indeed, in a way which is naturally compatible with polyhedral functions, we assume that the sets to which the state variables must belong in order to satisfy the finite-time stability requirement are boxes (or more in general polytopes) rather than ellipsoids. The main result, derived by using polyhedral Lyapunov functions, is a sufficient condition for finite-time stability of linear systems, which can also be used in the controller design context. Detailed analysis and design examples are presented to illustrate the advantages of the proposed methodology over existing methods.

LMI-based Algorithm for the Reconstruction of Biological Networks

Abstract: The general problem of reconstructing a biological network from temporal evolution data is tackled via an approach based on dynamical systems theory. In order to identify the dynamical model of the network an optimization algorithm, based on Linear Matrix Inequalities, is proposed. This approach allows to take into account, in the identification phase, both the experimental data and the a priori biological knowledge about the arcs of the network. Furthermore, the effectiveness of the proposed algorithm is improved by exploiting the assumption of scale-free structure, as usual in biological processes. The technique is validated against a well assessed case-study, that is the model of fission yeast cell cycle developed by Novak and Tyson.

Estimation of the Domain of Attraction of Equilibrium Points for Quadratic Systems: Application to Tumor Stability Analysis

Abstract: This paper considers the following problem: given an asymptotically stable equilibrium point of a nonlinear quadratic system, determine whether an assigned polytope surrounding the equilibrium point belongs to its domain of attraction. The proposed algorithm requires the solution of a feasibility problem that can be casted in terms of linear matrix inequalities constraints. In view of the important role played by quadratic models in systems biology, the work focuses on the application of the proposed technique for a quantitative study of the development of tumor phenomena in human beings.