Finite-time dissipative control for time-delay Markov jump systems with conic-type non-linearities under guaranteed cost controller and quantiser

For a class of conic-type non-linear time-delay Markov jump systems, the asynchronous dissipative output feedback controller based on the guaranteed cost control and quantiser is designed in this study. In real applications, the system and the controller modes are always non-synchronous, so we introduce the hidden Markov model to solve this problem. Furthermore, we define three novel auxiliary variables and use quantisers to accomplish the output feedback controller design. Then, the finite-time boundedness and strict dissipativity of the closed-loop systems are guaranteed by sufficient conditions, and the controller also meets the guaranteed cost-control performance. By solving a set of linear matrix inequalities, we get the controller gains, the guaranteed cost control performance index J*, and the dissipative performance index alpha. Finally, the correctness and feasibility of this designed approach are demonstrated by a given example.

Automated summary

In this study, an asynchronous dissipative output feedback controller was designed for a class of conic-type non-linear time-delay Markov jump systems, utilizing a hidden Markov model to address non-synchronous issues and quantisers for controller design. By solving a set of linear matrix inequalities, the finite-time boundedness and strict dissipativity of closed-loop systems were ensured, along with meeting guaranteed cost-control performance. The correctness and feasibility of this approach were demonstrated through a given example.