Design of reduced-order multiple observers 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 state reconstruction for Takagi-Sugeno fuzzy systems having unknown inputs and uncertainties. The new designed multiple observer is a combination of a typical reduced-order observer and a full-order multiple observer. The sufficient stability conditions of the observer are derived via the Lyapunov theory; to cancel the possible system’s uncertainties and to improve its robustness, some compensation terms have been added in the dynamics of the multiple observer. It will be shown that the problem of reduced-order multiple observers for Takagi-Sugeno fuzzy models with unknown inputs can be reduced to the standard case when the unknown inputs do not interfere in the equations of the observer. The main advantages of the new observer are: its simplicity (quantified in reduced implementation/computational complexity), the decrease of the necessary sensors’ number, a smaller number of existence conditions due to an iterative loop included in the observer’s design algorithm, and the avoidance of the pole placement technique. The suggested algorithm summarizing the steps of design procedure has been software implemented and validated for a concrete case (motion of an airplane during landing).