The effect of the elasticity of the water column in the penstock of a hydro power plant represents an irrational mathematical function. In this paper, this function is reduced to a lower order using the H-infinity approximant method. The gate position-turbine power nonlinear steady state characteristic is modeled by this reduced order function, and then, the time domain and frequency domain simulations of turbine power are presented and compared with the widely known Pade approximant method for order reduction of irrational functions. State estimation of the inelastic and elastic fifth order state space model of the hydro plant is also performed. The method adopted for state estimation is based on second order polynomial approximations of a multi-dimensional interpolation formula. It is found that the state estimation of the plant by this method outperforms the linear Kalman filter in terms of estimation. Then, a state estimation based linear quadratic (LQ) control approach for the hydro, turbine speed control is also presented. The simulated results are compared to the linear quadratic regulator that assumes all the states are measurable. (c) 2006 Elsevier Ltd. All rights reserved.