Reliable Robust Control Design for Uncertain Mechanical Systems

Abstract

In this article, we consider the problem of reliable Hâˆ‍ control for a class of uncertain mechanical systems with input timevarying delay and possible occurrence of actuator faults. In particular, we assume that linear fractional transformation (LFT) uncertainty formulations appear in the mass, damping, and stiffness matrices. The main objective is to design a state feedback reliable Hâˆ‍ controller such that, for all admissible uncertainties as well as actuator failure cases, the resulting closedloop system is robustly asymptotically stable while satisfying a prescribed Hâˆ‍ performance constraint. By constructing an appropriate Lyapunov–Krasovskii functional (LKF) and using linear matrix inequality (LMI) approach, a new set of sufficient conditions are derived in terms of LMIs for the existence of robust reliable Hâˆ‍ controller. Further, Schur complement and Jenson's integral inequality are used to substantially simplify the derivation in the main results. The obtained results are formulated in terms of LMIs which can be easily verified by the standard numerical softwares. Finally, numerical examples with simulation result are provided to illustrate the applicability and effectiveness of the proposed reliable Hâˆ‍ control scheme. The numerical results reveal that the proposed theory significantly improves the upper bound of time delays and minimum feasible Hâˆ‍ performance index over some existing works.