基于zonotope的离散时间Markov跳变系统的状态区间估计

State interval estimation of discrete-time Markov jump system-based on zonotope

为了有效地处理鲁棒估计产生的误差,为系统提供可靠的估计信息,针对一类具有未知输入的线性离散时间马尔科夫跳变系统(Markov jump systems,MJS),提出了一种新的状态区间估计方法。设计一个降维未知输入观测器,实现系统状态的观测,并以线性矩阵不等式的形式给出了观测器存在的充分条件,确保误差系统随机稳定,且具有较好的H∞干扰抑制性能。基于设计的降维未知输入观测器,提出了一种利用中心对称多胞体(zonotope)的方法来近似状态边界,从而获得系统状态的区间估计,使所获得的系统的状态值更加准确。通过一个数值仿真验证了所提方法的有效性。

In order to effectively deal with the error generated by robust estimation and provide reliable estimation information for the system,we propose a new interval estimation method for a class of linear discrete-time Markov Jump Systems(MJSs)with unknown inputs.First,a reduced-order unknown input observer is designed to realize the observation of the system state,and the sufficient conditions for the existence of the observer are given in the form of linear matrix inequality to ensure that the error system is stochastically stable and has good H??interference suppression performance.Then,based on the designed reduced-order unknown input observer,the zonotope method is used to approximate the state boundary to obtain the interval estimation of the system state.Finally,a numerical simulation verifies the effectiveness of the proposed method.