Interval Stabilization for Switched Stochastic Positive Systems: A State-Dependent Switching Scheme With Convergence Rate Constraint

This paper investigates the stability analysis and control design of a class of multi-interval switched stochastic positive systems (SSPSs) with state-dependent switching (SDS). Unlike existing research, this paper addresses switching systems where all subsystems are open-loop unstable, achieving not only system stability but also dynamic performance regulation. Notably, effective regulation of switching positive systems without external controllers presents inherent challenges. First, to overcome the difficulty of regulating SSPSs without controller design, a novel region partitioning is proposed using convex combination techniques. Second, a novel switching strategy is designed based on the system’s dynamic state, dynamically selecting the active subsystem according to real-time system conditions. Building upon this, a multi-interval regulation method is proposed. Specifically, by controlling the interval parameters of the maximum eigenvalue, the dynamic characteristics of each subsystem can be effectively coordinated, ensuring precise regulation of convergence speed. Finally, the effectiveness of the proposed technique is validated through a numerical example and the Black-Scholes model in the financial domain.