Stochastic hybrid systems with renewal transitions: moment analysis with application to networked control systems with delays (Q2840145)

SHS (stochastic hybrid systems) with \(n\)-dimensional real state space ``combine continuous dynamics and discrete logic'' in the following way: There is a finite set of modes the system may attain, changing modes depend deterministically on the present mode and state of the system at transition times. Inter-transition times are random, depending on the actual mode and are determined by a set of competing clocks, the minimal clock time determines the next transition instant.NEWLINENEWLINEThe development of the system between transition instants is determined by a linear (deterministic) differential equation, the differential operator is determined by the actual mode. Whenever a transition instant occurs the state of the system may be reset, depending again deterministically on the mode just before transition and the (number of the) clock which triggered the transition instant.NEWLINENEWLINEThe authors determine a set of Volterra equations to compute multidimensional mixed moments of the marginal state variables and provide numerical methods to solve the equations and discuss how to estimate from the obtained moments at time \(t\) the state distribution at time \(t\).NEWLINENEWLINEFurthermore, Lyapunov exponents of higher order are derived via root finding for a spectral equation.NEWLINENEWLINEAs an example the authors consider feedback control in a network control problem.