An argument-principle-based framework for structural and spectral characteristics in linear dynamical systems

By means of the argument principle in complex analysis, the paper proposes a novel complex geometric framework about structural features in terms of controllability/observability and stability/stabilisability, and spectral ones in terms of bounded/positive realness for transfer functions in linear dynamical systems. The proposed criteria render alternative complex/frequency-domain interpretations about the structural and spectral essentials. Moreover, the criteria are implementable graphically with locus plotting, independent of singularities distribution, locus orientation specification, singularity-related locus encirclement counting and prior frequency sweeping; the criteria are also utilisable numerically via complex argument increment integration without locus plotting, independent of iterative algorithms. In either ways, the criteria are numerically tractable and opt for robustness analysis and synthesis. Numerical examples are included to illustrate the main results.