Hybrid H 2 / H ∞ $$ {H}_2/{H}_{\infty } $$ Interval Observer Design for a Class of MIMO Nonlinear Systems With Interference Noise

An interval observer based on hybrid $H_2/H_{\infty }$ performance index is proposed for a class of multi-input multi-output (MIMO) nonlinear systems subject to external interference noise in this article. In this article, considering the effect of external interference noise on the nonlinear systems, the interval observer is constructed to obtain the system interval state for the MIMO nonlinear systems. Then, the interval observer gain is calculated by combining the hybrid $H_2/H_{\infty }$ performance index. The introduced method makes the interval width narrower and reduces the effect of external interference noise. The optimization problem is transformed into linear matrix inequalities. Eventually, the proposed method's theoretical viability has been demonstrated through Lyapunov stability theory. The efficacy of the proposed approach is substantiated through the robotic arm system. The approach making the interval observer obtained interval estimates with smaller interval widths.