Design of reduced-order interval observers for LTI systems with bounded time-varying disturbances: a parametric approach

Abstract

This paper investigates the design problem of reduced-order interval observers for linear time-invariant systems with bounded time-varying disturbances. Although there are many excellent design methods of interval observers, it is still a worth discussing problem to construct the cooperativity of observer error dynamics. Firstly, under the full consideration of anti-interference point, a general approach to design a reduced-order interval observer is proposed, and the complexity of constructing the system cooperativity is decreased. Secondly, a parametric design method of the reduced-order interval observers is further built on the above one by solving a type of generalised Sylvester equations, which ensures the existence of the reduced-order interval observers, and the calculation problem of linear matrix inequalities is avoided effectively. Besides, one further novelty is the consideration of the parameters whose influence on the observer performance, such as the convergence rate of the output interval and robustness. Meanwhile, a constructive procedure to obtain a reduced-order interval observer is advanced. Finally, the effectiveness of the proposed method is illustrated through numerical simulations.

Keywords:

• Reduced-order
• interval observer
• parametric approach
• time-varying disturbances

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by National Natural Science Foundation of China [61690210, 61690212].