Discrete Control Systems

The Lurie control system and the well-known Lurie problem were originally developed for solving the nonlinear systems described by ordinary differential equations (ODE), and the most research interest and results in this area were focused on ODE systems. With the very fast development of computer systems and technology, the dynamics and asymptotic behavior of discrete systems described by difference equations (DE) play more important roles in solving practical problems [115], attracting more and more researchers [47]. The absolute stability of discrete Lurie control systems is naturally raised. However, the results obtained so far for such systems are relatively less than that of continuous Lurie control systems.

In this chapter, we will generalize the recently developed theory and methodology for continuous Lurie control systems to study discrete Lurie control systems described by difference equations. We will mainly discuss the sufficient and necessary conditions of absolute stability, and some practically useful algebraic suffi- cient conditions of absolute stability. The material of this chapter is mainly chosen from [77, 84].