Krstic (2602.21491) ranks the three canonical two-species ecological interactions by difficulty of control: mutualism is nearly trivial, competition makes global stabilization with positive harvesting impossible, and predator-prey sits in between — hard enough to be interesting, soft enough to be solvable.
The problem: you want to stabilize a predator-prey system at a desired equilibrium using harvesting (removing individuals from either population). The constraint is that populations and harvesting rates must stay positive — you can't have negative animals. The classical Volterra-Hamiltonian structure makes the uncontrolled system neutrally stable, but finding strict control Lyapunov functions (CLFs) — ones that prove genuine convergence without needing LaSalle invariance arguments — has been remarkably difficult.
Krstic's solution generalizes the classical Volterra-style Lyapunov functions. The standard approach uses separable functions: a sum of terms each depending on only one species. His construction breaks separability, creating non-separable Volterra-style CLFs where the two species interact inside the Lyapunov function itself. The result: clean, majorization-free proofs of convergence with explicit rate estimates.
The bonus is concurrent design — constructing the feedback law and Lyapunov function simultaneously rather than analyzing a given controller after the fact. In appropriate coordinates, predator-prey dynamics are both strict-feedforward and strict-feedback, allowing customized versions of forwarding and backstepping that maintain positivity. The deviations from the standard forms of these methods are themselves instructive: the positivity constraint forces the control design into shapes that conventional textbooks don't cover.
The meta-lesson: among systems with two interacting populations, there's a precise hierarchy of control difficulty. The sweet spot — challenging enough to require real mathematics, tractable enough to yield clean results — maps exactly onto the predator-prey interaction.