Finite-time asynchronous H∞H∞ control for Markov jump repeated scalar non-linear systems with input constraints

• Finite time control issue for a quite comprehensive class of system model, that is, Markov jump repeated scalar nonlinear systems (MJRSNSs) has been addressed.
• An asynchronous controller is first proposed in MJRSNSs, which has less conservatism than mode-dependent when the partly available mode information is encountered.
• The input constraints associated with physical limitations in some practical applications have been fully considered, which make our model more realistic.

This paper is concerned with the problem of finite-time H∞H∞ control for Markov jump repeated scalar nonlinear systems (MJRSNSs) with input constraints. The jumps between MJRSNSs and desired mode-dependent controllers are considered to be nonsynchronous. The mode transition of the controllers is governed by a nonstationary Markov chain, which can model the different degrees of asynchronous jumps between MJRSNSs and controllers. With the aid of Lyapunov–Krasovskii methodology, some H∞H∞ performance criteria for the MJRSNSs are proposed. Based on these criteria, sufficient conditions on the existence of the desired controllers are established, and then the gains of the controllers can be obtained by solving a convex optimization problem. Finally, an example is presented to illustrate the effectiveness of our method.