Robust State Estimation for Linear Time-Varying Systems Using High-Order Sliding-Modes Observers

This chapter presents two algorithms for state estimation of linear time-varying systems affected by unknown inputs. The chapter is divided into two parts. The first part presents an observer for the class of strongly observable linear time-varying systems with unknown inputs. The proposed observer uses a cascade structure to guarantee the correct state reconstruction despite bounded unknown inputs and system instability. The second part of this chapter presents a finite-time observer that exploits the structural properties of the system through a linear operator. The particular design of this observer allows for avoiding the use of a cascade structure, providing with reduced complexity an exact estimate of the states after a finite transient time, even in the presence of possible instability of the system and the effects of bounded unknown inputs.