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math.OC2026
Spectral Decomposition of Discrete-Time Controllability Gramian and Its Inverse via System Eigenvalues
Alexey Iskakov
This paper develops a closed-form spectral decomposition framework for the Gramian matrices of discrete-time linear dynamical systems. The main results provide explicit decompositi…
math.OC2025
Spectral Decompositions of Controllability Gramian and Its Inverse based on System Eigenvalues in Companion Form
Alexey Iskakov, Igor Yadykin
Controllability and observability Gramians, along with their inverses, are widely used to solve various problems in control theory. This paper proposes spectral decompositions of t…
math.OC2019★ 4 cited
Lyapunov modal analysis and participation factors with applications to small-signal stability of power systems
Alexey B. Iskakov, Igor B. Yadykin
When random disturbances are regularly introduced into a dynamical system over time, its small-signal stability is determined by the energy of perturbations accumulated in the syst…