On Second-Moment Stability of Discrete-Time Linear Systems With General Stochastic Dynamics
Yohei Hosoe, Tomomichi Hagiwara
Abstract
This article provides a new unified framework for second-moment stability of discrete-time linear systems with stochastic dynamics. Relations of notions of second-moment stability are studied for systems with general stochastic dynamics, and associated Lyapunov inequalities are derived. The system dynamics may depend on any type of stochastic process in our framework. Our results for the unified framework can immediately lead us to more specific and tractable stability conditions when the underlying stochastic process is restricted to a more definite one. Usefulness of the developed framework is demonstrated through three selected applications.
Topics & Concepts
Moment (physics)Stochastic processStability (learning theory)Lyapunov functionMathematicsApplied mathematicsContinuous-time stochastic processDiscrete time and continuous timeSecond moment of areaDynamics (music)Linear systemControl theory (sociology)Mathematical optimizationComputer scienceNonlinear systemStochastic differential equationControl (management)Mathematical analysisClassical mechanicsPhysicsStatisticsQuantum mechanicsAcousticsMachine learningGeometryArtificial intelligenceStability and Control of Uncertain SystemsStability and Controllability of Differential EquationsControl and Stability of Dynamical Systems