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Many mainstream robust control/estimation algorithms for power networks aredesigned using the Lyapunov theory as it provides performance guarantees forlinear/nonlinear models of uncertain power networks but comes at the expense ofscalability and sensitivity. In particular, Lyapunov-based approaches rely onforming semi-definite programs (SDPs) that are (i) not scalable and (ii)extremely sensitive to the choice of the bounding scalar that ensures thestrict feasibility of the linear matrix inequalities (LMIs). This paperaddresses these two issues by employing a celebrated non-Lyapunov approach(NLA) from the control theory literature. In lieu of linearized models of powergrids, we focus on (the more representative) nonlinear differential algebraicequation (DAE) models and showcase the simplicity, scalability, andparameter-resiliency of NLA. For some power systems, the approach is nearlyfifty times faster than solving SDPs via standard solvers with almost no impacton the performance. The case studies also demonstrate that NLA can be appliedto more realistic scenarios in which (i) only partial state data is availableand (ii) sparsity structures are imposed on the feedback gain. The paper alsoshowcases that virtually no degradation in state estimation quality isexperienced when applying NLA.

On Scaling Robust Feedback Control and State Estimation Problems in Power Networks