Display omitted •Hierarchical robust switching control method with state vector matching is proposed.•Non-iterative Improved Moving Filaments method for plasma equilibrium reconstruction.•Plasma shape is controlled via Magnetic field at X-point and poloidal fluxes on the plasma separatrix.•Combination of advanced reconstruction code with isoflux control to achieve high performance.•New feedback control system simulation principle with LPV plasma model and reconstruction code. The paper describes a new hierarchical tokamak plasma shape control method implemented in the system with switching robust controllers and matching state vectors. A system robustness was achieved via the H∞ loop-shaping design. A novel modeling approach was used for the feedback system simulation: tokamak plasma equilibrium was calculated by the reconstruction code receiving the sum of experimental scenario signals and the output signals of a linear parameter varying (LPV) model, and sending the output to the multivariable plasma shape controller to close the loop. The LPV plant model is based on plasma equilibria reconstructed from the experimental data of the spherical tokamak Globus-M and is used to simulate plasma responses to small deviations from tokamak discharge scenario. The control system components were designed and combined to achieve high-performance operation during short pulses of plasma with total duration of about 200 ms and the divertor phase time length of 20–25 ms. The non-iterative Improved Moving Filaments method was developed for the plasma equilibrium reconstruction with the simultaneous determination of coordinates and currents of filaments. The plasma shape is controlled via the magnetic field at X-point and poloidal fluxes on a plasma separatrix, without calculation of the gaps between the plasma separatrix and the first wall. The hierarchical feedback control method was used in simulations of the entire plasma discharge with the transition from the limiter to the divertor plasma magnetic configuration. The control system was discretized and simulated on a high-speed computer to be prepared for application in Globus-M experiments by a real time test bed.