Proceedings of the 11 th International Conference of Control Systems, and Robotics (CDSR 2024) Chestnut Conference Centre - University of Toronto, Toronto, Canada – 10 -12 June, 2024 Paper No. 125 DOI: 10.11159/cdsr24.125 125-1 Stabilization of a Class of Discrete-Time Nonlinear Stochastic Systems Using Static Output Feedback Justin J. Kennah, Edwin E. Yaz, Susan C. Schneider Marquette University 1515 W. Wisconsin Ave., Milwaukee, USA justin.kennah@marquette.edu; edwin.yaz@marquette.edu; susan.schneider@marquette.edu Abstract - In this paper, static output feedback control is proposed to stabilize a general class of discrete-time stochastic nonlinear systems. Knowledge of the precise form of the nonlinearity or its statistics are not required. Instead, it is only necessary that a bound on the second moment of nonlinearity can be determined. The control gain is determined by solving a linear matrix inequality which is sufficient to show that the controlled system is stable in the mean square and almost sure senses. Keywords: Output Feedback; Nonlinear systems; Stochastic systems; Discrete-time systems; Linear matrix inequality 1. Introduction This paper considers static output feedback stabilizing control for a general class of discrete-time nonlinear stochastic systems given by the following equations +1 = + + ( , , ) (1) = (2) where ∈ℝ is the state, ∈ℝ is the input, ∈ℝ is an independent zero mean noise sequence, ∈ℝ is the output, and ( , , ): ℝ ×ℝ ×ℝ →ℝ is a nonlinear function satisfying the following properties (0,0, )=0 (3) {( , , )} = 0 (4) {( , , ) T ( , , )} = 0 ∀ ≠ (5) {( , , ) T ( , , )} ≤ ∑ ( T + T ) =1 (6) where {} denotes the expectation of conditional on , and = ( + 1)/2. Additionally, the matrix bounds , ∈ ℝ × , and ∈ℝ × , are known for all . Further, since Eqn. (6) represents the upper bound of a covariance relation, it follows that all matrices on the right-hand side of the inequality are symmetric and at least positive semidefinite. This particular class of systems, as pointed out in [1]-[4], is in fact quite general and includes several well-known systems such as linear systems with additive noise, linear systems with state and control multiplicative noise, state and control norm dependent random vectors, random vector dependent on the sign of a nonlinear function of the state, and many others. Several researchers have investigated this particular class of systems in the past. It was shown in [1] that the optimal finite horizon controller which minimizes a quadratic performance criteria, is a linear function of the states of the system. However, this method assumes perfect knowledge of the states of the system. Additionally, the form of the nonlinearity is