Modellistica ed analisi dei sistemi 2D con applicazioni alla codifica convoluzionale

Dottorato di ricerca in ingegneria dei sistemi. 7. ciclo. A. a. 1991-94. Tutore E. Fornasini. Coordinatore G. MarroConsiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7, Rome; Biblioteca Nazionale Centrale - P.za Cavalleggeri, 1, Florence / CNR - Consiglio Nazionale delle RichercheSIGLEITItal

Segnali e Sistemi

Terza edizion

Segnali e Sistemi

Seconda edizion

A stabilizable switched linear system does not necessarily admit a smooth homogeneous Lyapunov function

The contribution of this paper is twofold. Firstly, an example of a (positive) linear switched system that can be stabilized, via a controlled switching signal, but does not admit a smooth and positively homogeneous control Lyapunov function, is provided. The spectral properties of the subsystem matrices and of the Lyapunov candidates of the convex dierential inclusion associated with the switched system, are thoroughly investigated. Secondly, by taking inspiration from the example, new feedback stabilization techniques for stabilizable positive switched systems are provide

Co-positive Lyapunov functions for the stabilization of positive switched systems

In this paper, exponential stabilizability of continuous-time positive switched systems is investigated. For two-dimensional systems, exponential stabilizability by means of a switching control law can be achieved if andonly if there exists a Hurwitz convex combination of the (Metzler) system matrices. In the higher dimensional case, it is shown by means of an example that the existence of a Hurwitz convex combination is only sufficient for exponential stabilizability, and that such a combination can be found if and only if there exists a smooth, positively homogeneous and co-positivecontrol Lyapunov function for the system. In the general case, exponential stabilizability ensures the existence of a concave, positively homogeneous and co-positive control Lyapunov function, but this is not always smooth. The results obtained in the firstpartofthepaperare exploited to characterize exponential stabilizability of positive switched systems with delays, and to provide a description of all the “switched equilibrium points” of an affine positive switched system

Lyapunov stability analysis of higher-order 2D systems

We prove a necessary and sufficient condition for the asymptotic stability of a 2D system described by a system of higher-order linear partial difference equations. We show that asymptotic stability is equivalent to the existence of a vector Lyapunov functional satisfying certain positivity conditions together with its divergence along the system trajectories. We use the behavioral framework and the calculus of quadratic difference forms based on four-variable polynomial algebra