On the Maximal Output Admissible Set for a Class of Bilinear Discrete-time Systems

Given a discrete-time controlled bilinear systems with initial state x(0) and output function y(i), we investigate the maximal output set Theta(omega) = {x(0) is an element of Double-struck capital R-n, y(i) is an element of omega, for all i >= 0} where omega is a given constraint set and is a subset of Double-struck capital R-p. Using some stability hypothesis, we show that Theta(omega) can be determined via a finite number of inequations. Also, we give an algorithmic process to generate the set Theta(omega). To illustrate our theoretical approach, we present some examples and numerical simulations. Moreover, to demonstrate the effectiveness of our approach in real-life problems, we provide an application to the SI epidemic model and the SIR model.