Finite-time ℓ2–ℓ∞ control of Markovian jump linear systems with partly accessible hidden information via asynchronous output feedback

This work addresses the asynchronous finite-time ℓ₂-ℓ_∞ control problem for discrete-time Markovian jump linear systems (MJLSs) via static output feedback strategy. The asynchronous phenomenon between the system mode and controller mode is represented as a hidden Markov model. Compared with the existing literature, the strict assumption on the mode observation conditional probability matrix (MOCPM) of a hidden Markov model is removed in this work. By means of matrix inequality techniques, sufficient conditions are attained to ensure both of the finite-time stochastic boundedness and the finite-time ℓ₂-ℓ_∞ disturbance attenuation performance of the MJLSs subject to partly accessible MOCPM. Furthermore, an algorithm is established to solve asynchronous control gains. Finally, the multiplier-accelerator macroeconomic system is provided to illustrate the effectiveness and applicability of the proposed design scheme.