Robust stability of singularly perturbed descriptor systems with uncertain Markovian switchings and nonlinear perturbations

This paper is concerned with the problem of robust stability of Markovian jump singularly perturbed descriptor systems with uncertain switchings and nonlinear perturbations for any ϵ∈0,ϵ̄, where ϵ̄ is a pre‐defined positive scalar. A linear matrix inequality (LMI) condition is firstly established to guarantee the existence and uniqueness of a solution. Then, an ϵ‐independent condition in terms of LMI related to ϵ̄ is derived via using an ϵ‐dependent Lyapunov function, where the solution exists uniquely and is globally exponentially mean‐square stable simultaneously. Finally, numerical examples are used to show the feasibility and effectiveness of the given theoretical results.