# A state observer-based robust control method for perturbation-containing nonlinear discrete interconnected Systems

## TL;DR

This paper introduces a new robust control method for complex systems with disturbances, using a state observer to improve control performance.

## Contribution

A novel state observer-based control method for nonlinear discrete interconnected systems with disturbances is proposed.

## Key findings

- The proposed method allows separate design of observer and controller with guaranteed stability.
- The state observer's performance was enhanced by adding constraints on convergence rate.
- A numerical example verified the effectiveness of the separation design method.

## Abstract

In this study, the problem of the robust control of interconnected systems was investigated. A controller design method based on a state observer is proposed for nonlinear discrete interconnected systems with disturbance terms. In the proposed method, the observer and controller of the interconnected systems are designed separately, and sufficient conditions for the existence of the gain matrix are provided. In the design of the state observer, considering the convergence rate of the observation error, the performance of the state observer was improved by adding constraints. The influence of the external disturbance of the system on the state estimation is reduced by introducing a performance index, which provides the necessary theoretical basis for the design of the controller. In the controller design, based on the disk stability lemma and control theory, sufficient conditions for the existence of the controller are provided, and robust stabilization of the feedback closed-loop system was realized. In this study, the separate design method of the controller was compared with the centralized design method, which demonstrated the superiority of the separate design of the observer and controller. Finally, a numerical example is discussed, in which the separation design method of the robust controller was tested, and the effectiveness of the method was verified.