H∞ Control With Convergence Rate Constraint for Time-Varying Delay Switched Systems
针对平均驻留时间切换信号下的时变时滞切换系统，提出一种新的渐近稳定性判据，并设计H∞控制器以约束系统收敛速率，通过数值算例和水污染控制问题验证了方法的有效性。
This article emphasizes the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> control problem with convergence rate constraint for time-varying delay switched systems under the average dwell time switching signal. First, a novel criterion of asymptotic stability with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> performance is advanced by introducing the method of average dwell time and the definition of asymptotic interval stability, which is more exact than the general stability criterion in estimating the convergence of the systems. Next, the technique of structuring <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> controller is derived from the stability analysis described above, which can constrain the rate of the system to equilibrium, and make it content the preset <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> performance. Finally, a numerical calculation and a water pollution control issue demonstrate the functionality of the technique.