Finite‐Time Control for Uncertain Singular Systems With Nonlinear Repeated Scalars and Markovian Jumps

ABSTRACT This paper investigates the robust finite‐time control for uncertain discrete‐time singular systems with nonlinear repeated scalars and Markovian jump parameters. By employing the implicit function theorem and Lyapunov function approaches, sufficient conditions are derived to guarantee the regularity, causality, uniqueness of solutions in the neighborhood of the origin, singular stochastic finite‐time stabilization, and singular stochastic finite‐time stabilization for the addressed systems. According to the descriptor system approach, solvability criteria for these control problems are also established, which can be effectively converted into linear matrix inequalities. Additionally, the correctness and feasibility of the proposed method are demonstrated by numerical examples.