A Hybrid Proportional Impulsive Plus Integral Robust Control Algorithm for H∞ Stabilization

In this paper, the robust stabilization issues on uncertain system with H
_∞
performance are investigated by applying impulsive time related control algorithm. A hybrid control scheme is novelly proposed using proportional impulsive plus integral mechanism. This impulse-time-dependent (ITD) feedback controller employs the proportional control action K
_p
at impulse instants for stabilizing. Then, intermittently the integral control strategy K
_I
(t) is implemented between impulsive time intervals for improving the state convergence. Sufficient conditions are derived to ensure the closed-loop performance. In addition, a memory controller K
_D
is introduced to tackle the stabilization problem of system with signal transmission delay. Furthermore, a distributed time-varying delay δ
_k
(t) is defined in the impulsive control-based system. Considering discrete and distributed time-varying delays concurrently, the ITD stability criteria are deduced to guarantee the H
_∞
performance on uncertain system with exogenous disturbance. Numerical examples are conducted to show the expected stabilization and state convergence response with disturbance attenuation of this development.