Design of simultaneously stabilizing controllers and its application to fault-tolerant lane-keeping controller design for automated vehicles

Simultaneous stabilization deals with the following question: given a finite number of LTI plants P₁,P₂,...P_k does there exist a single LTI controller C such that each of the feedback interconnections (P_i,C) (i=1,2,...,k) is internally stable? This paper presents a new methodology for the design of simultaneously stabilizing controllers for two or more plants that satisfy a sufficient condition. A classic result from simultaneous-stability theory is invoked to cast the sufficient condition as a linear matrix inequality (LMI). It is shown that in this setting, the problem of design of simultaneously stabilizing controllers can be reduced to that of a standard H_∞ control problem. The technique developed is applied to the design of a fault-tolerant controller for lane-keeping control of automated vehicles. The controller makes the system insensitive to a failure in either one of two lateral error measuring sensors used for lane-keeping control. Experimental results confirm the efficacy of the design and reinforce analytical predictions of performance.