Impulsive Observer of Linear Systems: An Adaptive Impulsive Gain Approach

This article provides a new impulsive observation approach [called impulsive adaptive observer, impulsive adaptive observation (IAO)] for a class of linear systems. A discrete-time-based adaptive rule for the impulsive observer gain is designed using only output information at discrete-time intervals (or impulsive instants), overcoming the real-time data requirement of continuous-time adaptive observation frameworks. The IAO effectively estimates the states of a continuous-time system and demonstrates outstanding state tracking performance in practical implementations. Furthermore, the IAO-based feedback controller is designed to stabilize the controlled plant. Stability criteria for the IAO protocols are established, showing improved performance over existing schemes by reducing computational load and enhancing control flexibility. The simulations for the electrical system are presented finally to confirm the effectiveness of the IAO and its control approach.