Simultaneous Estimation of the State, Unknown Input, and Output Disturbance in Discrete-Time Linear Systems

Abstract

A state observer and unknown input and output disturbance estimators are proposed for discrete-time linear systems corrupted by bounded unknown inputs and output disturbances. Necessary and sufficient conditions for the existence of the state observer and disturbance estimators are given. Relationships with the strong observer of Hautus are investigated. The state, unknown input, and output disturbance estimation errors are guaranteed to be <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{\infty }$</tex-math></inline-formula> -stable with prescribed performance level. The design of the state observer and disturbance estimators are given in terms of linear matrix inequalities. The proposed estimators can be applied to detect adversarial attacks on the communication channels between the controller and actuators and between the plant sensors and the controller.