H∞ fuzzy control of semi-Markov jump nonlinear systems under σ-error mean square stability. Issue 11 (18th August 2017) - Yang, Ting; Zhang, Lixian; Lam, Hak-Keung
ABSTRACT: This paper is concerned with the problem of time-varying H ∞ fuzzy control for a class of semi-Markov jump nonlinear systems in the sense of σ-error mean square stability. The nonlinear plant is described via the Takagi–Sugeno fuzzy model. By defining a time-varying mode-dependent Lyapunov function, a set of sufficient stability and stabilisation criteria for non-disturbance case is first derived and then applied to the investigation of H ∞ performance analysis and H ∞ fuzzy controller design problems of semi-Markov jump nonlinear systems. Different from the traditional stochastic switching system framework, the probability density function of sojourn time is exploited to circumvent the complex computation of transition probabilities. The derived conditions can cover the time-invariant mode-dependent and time-invariant mode-independent H ∞ fuzzy control schemes as special cases. A classic cart-pendulum system is presented to demonstrate the effectiveness and advantages of the proposed theoretical results.