Reduced-order multiple observer for Takagi–Sugeno systems with unknown inputs

Abstract

The paper discusses a niche area problem — the design of reduced-order multiple observers which can achieve the finite-time state reconstruction for Takagi–Sugeno multiple models with unknown inputs. The new reduced-order multiple observer obtained in this paper is only the second ever designed, the author of this paper continuing his work started one year ago with the introduction of the reduced-order multiple observer concept. The obtaining of the new reduced-order multiple observer is achieved by combining two classical reduced-order observers for linear time-invariant multivariable systems with unknown inputs and a full-order multiple observer for Takagi–Sugeno systems. The main innovative idea behind the design of the reduced-order multiple observer for Takagi–Sugeno systems described by the multiple models is the split of the multiple model into two subsystems: an unknown-input-free subsystem and an unknown-input-depending subsystem. The unknown-input-free subsystem is brought to the form of a standard multiple model and, in this situation, any algorithm to design full-order multiple observers can be used in the design of reduced-order multiple observers. The steps of the design procedure have been summarized and software implemented; then, the validation of the suggested algorithm has been done for two concrete cases associated to the motion of an aircraft during its landing