On the stability and control of the Schimizu-Morioka system of dynamical equations N. Islam, H. P. Mazumdar and A. Das Abstract. In this paper, the stability analysis of the Schimizu-Morioka system of dynamical equations is performed by applying the Routh-Hurwitz criterion to the solutions of the system near to equilibrium points. The control analysis of the linearized version of the system of equations is then made by adding a control term. As well, phase portraits are analyzed in terms of values of a control parameter. M.S.C. 2000: 37N35, 37L15, 37B25, 34D20. Key words: Schimizu-Morioka dynamical equations, equilibrium points, Lyapunov stability, Routh-Hurwiz criterion, control parameters. 1 Introduction Schimizu-Morioka [9] constructed a model system by dynamical equations which received much attention due to its ability to describe bifurcation of the associated Lorenz like attractors. The model is described by the dynamical system (1.1)    ˙ X = Y ˙ Y = X − λY − XZ ˙ Z = −αZ + X 2 , where α, λ > 0. They studied the complex behavior of the trajectories of the system by means of computer simulation. The system of equations (1.1) was used as a model to investigate the well known Lorenz system [6, 4] for the cases when the Rayleigh number is large. Shilnikov [7, 8] pointed out that the boundary of the region of existence of a Lorenz like attractor includes two 2-dimensional points, say Q σ (α =0.608,λ = 1.0499) and Q A (α =0.549,λ =0.605). Recently, Kozlov [5] presented an algorithm for the construction of solutions of the ordinary differential equations with power asymptotics. He also applied the technique involved in it to study the stability of the system. Chernousko et al. [3] presented the method of dynamical system’s phase state evaluation and building of control laws on the basis of the estimates. Controlled dynamical systems subject to perturbations are considered under uncertainties and Differential Geometry - Dynamical Systems, Vol.11, 2009, pp. 135-143. c  Balkan Society of Geometers, Geometry Balkan Press 2009.