Design of a common observer for two linear systems with unknown inputs

This paper considers the design of a common linear functional observer for two linear time-invariant systems with unknown inputs. A structure for a common observer which only uses the available output information is proposed. Here, for the proposed structure, we show that the simultaneous functional observation problem of two plants is reduced to a problem of designing two observers: the first is a full-order unknown input observer of one of the two systems; the second observer is a common unknown input observer of a system comprises two-connected systems. In general, the existence conditions for the second observer are very difficult to satisfy. This paper thus concludes that it is indeed very difficult to find a common observer for two linear systems with unknown inputs.<br /

LMI-Based Reset Unknown Input Observer for State Estimation of Linear Uncertain Systems

This paper proposes a novel kind of Unknown Input Observer (UIO) called Reset Unknown Input Observer (R-UIO) for state estimation of linear systems in the presence of disturbance using Linear Matrix Inequality (LMI) techniques. In R-UIO, the states of the observer are reset to the after-reset value based on an appropriate reset law in order to decrease the $L_2$ norm and settling time of estimation error. It is shown that the application of the reset theory to the UIOs in the LTI framework can significantly improve the transient response of the observer. Moreover, the devised approach can be applied to both SISO and MIMO systems. Furthermore, the stability and convergence analysis of the devised R-UIO is addressed. Finally, the efficiency of the proposed method is demonstrated by simulation results