Small Gain and Small Angle Conditions for Feedback Stability Analysis of Linear Stochastic Systems

In this paper, we formulate feedback control problems involving stochastic systems and stochastic signals and obtain stability conditions based on the notions called gains and angles. The family of systems under investigation is represented by a discrete-time linear time-varying stochastic (LTVS) model which generalizes the intensively studied multiplicative stochastic model. Such formulation may incorporate widely encountered networked control problems involving fading and packet-drop communication channels. For resolving feedback stability problems of LTVS systems, small gain and small angle conditions are proposed, and illustrative examples are presented.