Finite Time H2/H∞ Control for Piecewise Homogeneous Incomplete Mean‐Field Markov Jump System

This paper investigates the finite‐time control problem for mean‐field Markov jump systems (MFMJSs) with incomplete information. The incomplete information of the considered system is characterized by various uncertainties and time‐varying features of the transition probabilities (TPs), which makes the established system model more practical and general. First, sufficient conditions are derived to ensure the finite‐time stochastic stability of such MFMJSs. Second, the stochastic control problem is transformed into an ‐suboptimal zero‐sum game problem. Meanwhile, sufficient conditions based on linear matrix inequalities (LMIs) are derived to establish the finite‐time bounded real lemma for MFMJSs. Third, combined with ‐suboptimal non‐zero‐sum game theory, the finite‐time control problem is further addressed. Several sufficient stability conditions, the upper bound of the cost function, and the explicit forms of the control strategies are simultaneously obtained. In addition, a novel bilinear iterative algorithm is designed to handle inherent nonlinear terms, minimize the cost function, and expand the feasible domain of the parameters. Finally, a numerical example of a production‐inventory system is provided to illustrate the validity and correctness of the developed theoretical results.