Asynchronous dissipative control design for semi-Markovian jump systems with uncertain probability distribution functions of sojourn-time

Abstract This paper is concerned with the problem of asynchronous mode-dependent dissipative control for continuous-time semi-Markovian jump systems (S-MJSs), where the probability distribution functions of sojourn-time are established in a generic form to cover uncertainties that occur due to experimental limitations and errors. Further, based on a control-mode-dependent Lyapunov function, this paper proposes a robust control design method developed such that 1) the control system performance can be further improved compared to using system-mode-dependent Lyapunov functions, 2) the block size of stabilization conditions can be reduced, and 3) the non-convex terms combined with either positive or negative transition rates can be explicitly addressed. Finally, three illustrative examples are given to show the effectiveness of the proposed method.