Two‐Degree‐Of‐Freedom‐Based Feedback Control Design for Semi‐Markovian Jump Systems via Quadratic Function Negative Determination Approach

ABSTRACT This article addresses a state tracking control problem for a class of semi‐Markovian jump linear systems (SMJLSs) with time‐varying delays, uncertainties, and disturbances. In order to achieve the desired tracking performance, a lumped disturbance estimator manages the effects of disturbance signals and uncertainties while simultaneously estimating the unknown external input signal through the proper bandwidth selection of the low‐pass filter and model perturbations. Then, a quadratic delay product term is then incorporated into the construction of an suitable Lyapunov–Krasovskii functional candidate. In order to guarantee the stability of the examined SMJLSs under the proposed two‐degree‐of‐freedom‐based control, adequate conditions are derived in the form of linear matrix inequalities using the generalized reciprocally convex combination lemma. Finally, simulation results and comparative results are given to illustrate the effectiveness and advantages of the proposed control scheme.