Applying negative imaginary systems theory to non-square systems with polytopic uncertainty

This paper aims to apply Negative Imaginary (NI) systems theory non-square LTI systems, for example, flexible structure with redundant sensors and actuators. The proposes static pre- post-compensation schemes transform stable fat (i.e. no. of inputs more than the outputs) tall outputs inputs) plants into class Strongly Strict (SSNI) a subset Strictly (SNI) systems. proposed compensators can also stabilise or non-NI square plant in positive feedback loop. Moreover, be utilised design simple constant reference tracking scheme exploiting integral controllability propoerty SSNI Subsequently, observer-based post-compensators are developed handle cases when some system states not available direct measurement. Then, compensation extended stable, polytopic uncertainty. Finally, technique is applied tall/square uncertain preceded by slope-restricted nonlinearity.