Event-Triggered State and Disturbance Estimation for Lipschitz Nonlinear Systems With Unknown Time-Varying Delays

We consider the event-triggered state and disturbance simultaneous estimation problem for Lipschitz nonlinear systems with an unknown time-varying delay in the state vector. For the first time, state and disturbance can be robustly estimated by using an event-triggered state observer. Our method uses only information of the output vector when an event-triggered condition is satisfied. This contrasts with previous methods of simultaneous state and disturbance estimation based on augmented state observers where the information of the output vector was assumed to be always continuously available. This salient feature, thus, lessens the stress on communication resources while can still maintain an acceptable estimation performance. First, to solve the new problem of event-triggered state and disturbance estimation, and to tackle unknown time-varying delays, we propose a novel event-triggered state observer and establish a sufficient condition for its existence. Then to overcome some technical difficulties in synthesizing observer parameters, we introduce some algebraic transformations and use inequalities, such as the Cauchy matrix inequality and the Schur complement lemma to establish a convex optimization problem in which observer parameters and optimal disturbance attenuation levels can be systematically derived. Finally, we demonstrate the applicability of the method by using two numerical examples.

Automated summary

This paper addresses the simultaneous estimation problem of event-triggered state and disturbance for Lipschitz nonlinear systems with an unknown time-varying delay. State and disturbance can be robustly estimated using an event-triggered state observer, which only requires the output vector information when an event-triggered condition is met. Unlike previous methods, which assume continuous availability of the output vector information, this approach reduces the stress on communication resources while maintaining acceptable estimation performance. A novel event-triggered state observer is proposed, and a sufficient condition for its existence is established. By introducing algebraic transformations and utilizing inequalities, a convex optimization problem is formulated to derive observer parameters and optimal disturbance attenuation levels. The applicability of the method is demonstrated through numerical examples.