Abstract
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.
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