Periodically intermittent finite-time bounded control and <i>L</i> ₂ -gain analysis of switched delay nonlinear systems

This paper investigates the finite-time boundedness and weighted <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>L</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> -gain problem of switched nonlinear systems with constant time delay. In a periodic intermittent control framework, sufficient criteria are established to guarantee that the resulting closed-loop switched nonlinear systems can achieve finite-time boundedness and possess a finite-time weighted <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>L</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> -gain. The proof utilizes piecewise Lyapunov functions, formulating the conditions as a convex optimization problem solvable through linear matrix inequality techniques. Finally, numerical simulations are conducted to validate the efficiency of the methods.