This paper presents H∞ Filter SLAM, which is also known as the minimax filter to estimate the robot and landmarks location with the analysis on partial observability. Some convergence conditions are also presented to aid the analysis. Due to SLAM is a controllable but unobservable problem, it's difficult to estimate the position of robot and landmarks even though the control inputs are given to the system. As a result, Covariance Inflation which is a method of adding a pseudo positive semidefinite(PsD) matrix is proposed as one approach to analyze Partial Observability effects in SLAM and to reduce the computation cost. H∞ Filter is capable of withstand non-gaussian noise characteristics and therefore, may provide another available approach towards SLAM solution.