A BLMI-Based Framework for Robust Stabilization of Stochastic Hybrid Systems Under Dual-Mode Uncertainties

This study investigates the robust stabilization problem for linear stochastic hybrid systems (SHSs) characterized by dual uncertainties: parametric variations in system matrices and bounded uncertainties in Markovian transition rates. Novel sufficient conditions for exponential mean-square stability are derived via bilinear matrix inequalities (BLMIs). A systematic methodology is proposed to design robust state-feedback controllers, eliminating reliance on exact transition rate knowledge. Numerical simulations confirm the frameworks efficacy, demonstrating its applicability in scenarios with coexisting parametric and structural uncertainties.