Input-to-state stable nonlinear filtering for a class of continuous-time delayed nonlinear systems

Abstract

This paper investigates the input-to-state stable (ISS) nonlinear filtering problem for a class of continuous-time delayed nonlinear systems with external disturbance. A new delay-dependent nonlinear ISS filter is established through available measurements to estimate the states of delayed nonlinear systems, such that the filtering error system is both exponentially and input-to-state stable for any bounded external disturbance. The design of the nonlinear ISS filter for these nonlinear systems is achieved by solving a linear matrix inequality (LMI), which can be easily facilitated by using standard numerical packages. An illustrative example is given to demonstrate the effectiveness of the proposed filter.

Keywords:

• input-to-state stability (ISS)
• robust filtering problem
• delayed nonlinear system
• linear matrix inequality (LMI)
• Lyapunov–Krasovskii stability theory