Dissipativity-Based Integral Sliding Mode Control of Fuzzy Switched Positive Systems With Bumpless Transfer Performance

Abstract

Nonlinear switched positive systems (SPSs) subject to time-varying delays are ubiquitous in actual applications, whose control and synthesis are complicated due to the influence of positivity constraints, switching laws, and time delays. This article addresses the issues of dissipative sliding mode control and dissipativity-based sliding mode tracking control for fuzzy SPSs in the presence of time-varying delays under a state-dependent switching paradigm. First, a bumpless transfer technique and a hysteresis switching mechanism for fuzzy switched systems are employed to mitigate input chattering and avoid high-frequency switching, respectively. Then, a novel fuzzy integral switching sliding surface is formulated to accommodate the characteristics of nonlinear switched systems. Based on the multiple linear copositive Lyapunov function, sufficient conditions are derived to guarantee that the closed-loop positive system is asymptotically stable with strict $(q,r)$-$\alpha$ dissipativity and bumpless transfer performance under the proposed controller. Furthermore, the dissipative tracking control design is investigated via the designed fuzzy integral sliding mode surface, with guaranteed reachability under positivity and stability conditions. Ultimately, the feasibility of the mentioned fuzzy sliding mode control strategy is verified through two examples with a Lotka–Volterra population model.