Switched delay-dependent control policy for water-quality systems

A delay-dependent analysis and synthesis approach is established for a class of linear discrete-time switched systems with time-varying delays using switched Lyapunov-Krasovskii functionals (SLKFs). The problem of water-quality control is cast as the problem of delay-dependent L₂ gain analysis and synthesis. New delay-dependent asymptotic stability criteria are developed under arbitrary switching based on appropriately constructed SLKFs. Delay-dependent switched control feedback is then designed, based on state- and output-measurements, to render the corresponding switched closed-loop system delay-dependent asymptotically stable with a prescribed L₂ gain measure. The developed results are cast as linear matrix inequalities and tested by Matlab simulation on a representative water-quality example.