Asynchronous H∞ observer-based control synthesis of nonhomogeneous Markovian jump systems with generalized incomplete transition rates

Highlights：

• To cover a wide range of applications in the continuous-time MJS domain, this paper focuses on dealing with realistic problems that explore the emergence of nonhomogeneous Markov processes and asynchronous control mode, which have been largely excluded from previous studies. Further, this paper formulates both the observer and controller as subject to the asynchronous control mode because if the controller cannot measure the correct system mode, it is also difficult for the observer to use it to estimate the system state.

• When designing an asynchronous control via the system mode-dependent Lyapunov function approach, it is necessary to separate the Lyapunov matrix from the control gain in the stabilization condition. Thus, this paper proposes a state extension method as one possible way to achieve this separation while improving the control performance without using the aforementioned separation method.

• Due to the presence of time-varying transition rates, the asynchronous observer-based stabilization conditions result in an infinite number of LMIs. Thus, to overcome these difficulties, this paper offers a less conservative relaxation technique that can transform the stabilization conditions into a finite number of LMIs under boundary constraints of the transition rates. Especially, the proposed relaxation technique is devised in a way that can further reduce the computational complexity compared to the existing similar techniques.

• In general, the asynchronous observer-based stabilization condition is given in a nonconvex form because the exact system dynamics cannot be reflected in the output-feedback control. Thus, to cover this nonconvex problem, this paper proposes a two-step approach that can design an observer-based control by establishing one Lyapunov function for the entire state of the closed-loop control system.