Design of H∞-based sampled-data control for fuzzy Markov jump systems with stochastic sampling

Abstract

Abstract This paper concentrates on analyzing the stability problem for fuzzy Markov jump systems (FMJSs) via stochastic sampling and H ∞ -based sampled-data control scheme. With the help of input-delay technique, the probabilistic sampling intervals are reconstructed into a continuous time-varying system under stochastic parameters in the system matrices. Subsequently, a set of sufficient conditions ensuring the stochastic stability of the addressed FMJS with an allowable H ∞ disturbance attenuation value is formulated in the form of linear matrix inequalities (LMIs) by choosing a proper Lyapunov–Krasovskii functional involving triple integral terms and utilizing Wirtinger-based integral inequality. The desired sampled-data control gain can be determined in terms of the solution to the obtained LMIs. Lastly, the developed theoretical results and the benefits of the desired controllers are verified through numerical examples including a single link robot arm system.