H∞ state tracking control for a class of discrete-time Markov jump systems with packet loss and input saturation

The <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>∞</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> state tracking controller design method for a class of discrete-time Markov jump systems(MJS) with partially unknown transition probabilities and input saturation is proposed in this work. Firstly, considering the possibility of packet loss in the communication process of the system state and target state, a forecasting model is established. Then, based on forecasting model, a state tracking controller is further designed to achieve state tracking of multiple targets and achieve the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>∞</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> performance indicator. Finally, some sufficient conditions are provided to ensure the solvability of the above problem, and the correctness of the proposed method is verified by tracking sine signal, and ramp signal through two numerical examples.