A Parametric Approach to Design Interval Observers for Linear Systems with Time-Varying Disturbances

The design problem about interval observers for linear systems with time-varying disturbances is considered in the paper. With the nonsingular matrix transformation, the problem about solving the observable gain matrix complicatedly or the situation of nonexistent such matrix is efficiently solved by transforming it into the solution for a type of generalized Sylvester equations. Moreover, the specific parametric forms for the observable gain matrix and the nonsingular matrix are obtained by solving the generalized Sylvester equation. Further, a novel parameterized approach to design interval observers for linear systems with time-varying disturbances is proposed, and the output interval can be towards a constant with a desired convergence rate. Finally, a numerical example illustrates the efficiency of the proposed method.

1 Introduction

As known, in the control system synthesis and design, such as state feedback control or fault diagnosis, the need of observation of the physical states is of primary significance. However, it is unrealistic to obtain all state variables of the control systems in many practical situations. Therefore the concept of state reconstruction, namely observer design problem is put forward. A state observer as an auxiliary dynamical system mirrors the behavior of the control system. By the observer, the corresponding control strategies are implied, and the contradiction among irreplaceability in performance and the physical impossibility is solved.