Output Strictly Passive $${{\varvec{H}}_\infty }$$H∞ Control of Discrete-Time Linear Switched Singular Systems Via Proportional Plus Derivative State Feedback

This work aims to study the problem of output strictly passive $$H_\infty $$ control for discrete-time linear switched singular systems. By using multiple storage functions and iteration technique, some sufficient conditions are obtained based on output strict passivity and proportional plus derivative state feedback, which can guarantee that the closed-loop systems are normal and stable and satisfy a given $$H_\infty $$ performance. Proportional plus derivative state feedback sub-controllers with explicit expressions are designed. Proportional plus derivative state feedback can not only eliminate impulse phenomena, but also eliminate state jumps caused by incompatible initial conditions of subsystems at switching instants. A numerical example is given to verify the applicability of the results.