Finite-time resilient L2-L∞ control for semi-Markov jump systems with disturbances

This paper investigates the issues of finite-time <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant="script">L</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> - <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="script">L</mml:mi> <mml:mi>∞</mml:mi> </mml:mrow> </mml:math> boundedness and resilient control for a class of Semi-Markov jump systems (SMJSs) with disturbances. By conducting an analysis on the finite-time <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant="script">L</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> - <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="script">L</mml:mi> <mml:mi>∞</mml:mi> </mml:mrow> </mml:math> boundedness of stochastic SMJSs, we established a series of sufficient conditions to ensure the desired boundedness property. In light of uncertainties present in both the system dynamics and the external environment, mode-dependent resilient controllers are proposed for the boundedness of the uncertain system. The system’s modal switching is regulated by an SMJS. The developed resilient control strategy is designed to attenuate the peak magnitude of the system output, thereby attenuating or even eliminating the detrimental effects caused by abrupt external disturbances. Finally, a numerical example of a quadrotor unmanned aerial vehicle (UAV) altitude control system is included to illustrate the performance of the presented control strategy.