Asynchronous observer design for switched T-S systems with unmeasurable premises and switching mismatches

摘要

This paper investigates the design of asynchronous switched observers for continuous-time nonlinear switched systems, where Takagi-Sugeno fuzzy models represents the nonlinear modes, with mismatching switching laws and bounded output disturbances (e.g. representing measurement bias, noise or fault). The proposed switched T-S observers allow state estimations when the systems' premise variables are not necessarily measurable and when the observer's active switched-mode does not necessarily match the one of the switched system. To derive the design conditions, a multiple Lyapunov function candidate is considered to cope with the asynchronous switching modes, together with a H_∞ criterion to minimize the transfer between the output disturbance and the state estimation errors. Moreover, Lipschitz constraints are considered to cope with the unmeasurable premise variables. The proposed conditions are declined into four theorems as Linear Matrix Inequalities. Despite their increasing computational cost, these theorems bring successive conservatism improvements, allowing the users to select the appropriate conditions regarding to the complexity of their applications. Finally, an academic example and a practical one (dealing with a tunnel diode circuit) are given to compare the conservatism and to illustrate the effectiveness of the proposed asynchronous switched T-S observer design methodologies.