State feedback fuzzy-model-based control for discrete-time markovian jump nonlinear systems with time-varying delays

Abstract

In this paper, the stability analysis and stabilization problem for a discrete-time Markovian jump nonlinear systems (MJLNS) with time-varying delays are investigated. The timedelay is considered to be time-varying and has a upper bound. The transition probabilities of the mode jumps are considered to be completely known. Sufficient conditions for stochastic stability of the markovian jump fuzzy systems (MJFS) are derived via the linear matrix inequality (LMI) formulation, and the design of the stabilizing controller is further given. A numerical example is used to illustrate the developed theory. Index Terms-Linear matrix inequality (LMI), Markovian jump nonlinear sytems (MJLNS), stochastic stability, timevarying delays

Feedback predictive control for constrained fuzzy systems with Markovian jumps

“…However, despite these efforts, the issue of MPC for nonlinear MJS such as Samuelson multiplier accelerator economic model 23, tunnel diode circuits 24, 25, series of dc motor 26 and single‐link robot arm 27, has not been fully investigated and very few results are available. Moreover, most of the existing results refer to the nonlinear MJS which is based on the fuzzy modeling method mainly focusing on the H ∞ controller or filter design 28, 23–26, stability and stabilization analysis 27, 29–32, etc.…”