Event-Based Asynchronous H∞ Control for Nonhomogeneous Markov Jump Systems With Imperfect Transition Probabilities

Area of Science:

• Control Theory
• Systems Engineering
• Stochastic Systems

Background:

• Investigates event-based H∞ control for nonhomogeneous Markov jump systems (MJSs).
• Addresses challenges of partially unknown transition probabilities (TPs) and imperfect mode observation via Hidden Markov Models (HMMs).
• Considers a general scenario with a higher-level chain governing system TP matrix switching.

Purpose of the Study:

• To design an event-triggered asynchronous controller for MJSs with partially unknown TPs.
• To ensure stochastic stability and H∞ performance for the closed-loop system.
• To reduce communication network load using an event-triggered mechanism (ETM).

Main Methods:

• Employs a Hidden Markov Model (HMM) for system mode observation.
• Utilizes an observed-mode-dependent event-triggered mechanism (ETM) for controller design.
• Establishes sufficient conditions for stability and H∞ performance.

Main Results:

• Develops an event-based H∞ control strategy for nonhomogeneous MJSs with partially unknown TPs.
• Guarantees stochastic stability and prescribed H∞ performance for the closed-loop system.
• Demonstrates effectiveness through two illustrative examples.

Conclusions:

• The proposed method effectively addresses the event-based H∞ control problem for complex MJSs.
• The asynchronous controller design balances performance with communication efficiency.
• The framework is applicable to systems with partially unknown transition probabilities and imperfect mode detection.