Interval observer design for linear discrete switched systems

In order to solve the state interval estimation problem of linear switched systems, an interval observer is designed based on the original coordinate system, which can give the estimation of the upper and lower boundaries of the system. Firstly, an interval observer is constructed for the switched system, which can estimate the upper and lower boundaries of the state respectively. Secondly, the bounded disturbance and measurement noise vector of the system are regarded as augmented state variables, and the augmented system is constructed. On the basis of the augmented system, more parameter design degrees of freedom are introduced to reduce the design constraints and conservatism of the interval observer, so that the estimation error has good robustness to disturbances. under the switching signal satisfying the average dwell time constraint, the multi Lyapunov function approach is used to make the switching system globally exponentially stable and meet the weighted H_\infty performance index. Then the linear matrix inequality is solved to obtain the interval observer parameters and gain matrix of the switched system, so as to effectively obtain the accurate state boundary estimation of the system. Ultimately, a mathematical emulation example proves the effectiveness of the interval observer method.