Guaranteed H∞ Performance of Switched Systems with State Delays: A Novel Low-Conservative Constrained Model Predictive Control Strategy

Abstract

In this paper, for the first time, a simultaneous design of a model predictive control plan and persistent dwell-time switching signal utilizing the conventional multiple Lyapunov–Krasovskii functional is proposed for linear delayed switched systems that are affected by physical constraints and exogenous disturbances. The conventional multiple Lyapunov–Krasovskii functional with a ‘jump high’ condition is used as a step forward to reduce the strictness of constraints on controller design compared with the switched Lyapunov–Krasovskii functional. However, a dwell-time constraint is inflicted on the switching signal by the ‘jump-high’ condition. Therefore, to decrease the dwell-time limit, the persistent dwell-time structure is used and compared with other structures. Also, a new online framework is proposed to reduce the number of constraints on controller design at each time step. Moreover, for the first time, exogenous disturbances are considered in the procedure of MPC design for delayed switched systems, and non-weighted H∞ performance is ensured. The simulation outcome demonstrates the great performance of the suggested plan and its ability to asymptotically stabilize the switched system.

Keywords

• linear delayed switched systems
• model predictive controller
• multiple Lyapunov–Krasovskii functional
• persistent dwell-time
• H∞ performance