On the Crossing-Time for Two-dimensional Piecewise Linear Systems

GARCIA, A., S. BIAGIOLA, L. CASTRO, J. L. FIGUEROA AND O. AGAMENNONI

Iasi, Rumania

Conferencia; International Conference on Applied Analysis and Differential Equations; 2006

Faculty of Mathematics, University "Al. I. Cuza" of Iasi and Institute "Octav Mayer" of the Romanian Academy

Piecewise Linear (PWL) models have proved to be a useful tool for the approximation of nonlinear dynamical systems. The dynamics of the real physical system is approximated in a region of interest. For this goal, a finite number of simplices is used when a PWL model is chosen. The PWL systems is given by a linear time invariant system, which varies from one simplex to the other. A relevant topic when using PWL models is the determination of the state of the system when the trajectory crosses from one simplex to another one. An equivalent dilemma is the calculus of the time value at which this crossing takes place. In this paper, we provide a formula for determining the crossing time (CT) when a given linear time invariant system reaches a frontier between simplices. Explicit expressions for the R2 case are derived and some examples are presented.