H_∞ Control With Convergence Rate Constraint for Time-Varying Delay Switched Systems

This article emphasizes the $H_{\infty }$ 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 $H_{\infty }$ 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 $H_{\infty }$ 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 $H_{\infty }$ performance. Finally, a numerical calculation and a water pollution control issue demonstrate the functionality of the technique.