Linear matrix inequality approach to robust emergency lateral control of a highway vehicle with time-varying uncertainties

New linear-matrix-inequality (LMI) based methods are developed for the static-output-feedback stabilization and reduced-gain static-output-feedback stabilization of time-invariant systems. Unlike previous methods, the static-output-feedback method is non-iterative in LMI solutions. The methods are extended to design robust static-output-feedback controllers for time-varying systems using a polytopic-systems approach. Examples are given which demonstrate the use of each of the new methods. The specific problem of emergency lateral control of a highway vehicle is then addressed using the new robust static-output-feedback method. A controller is designed which robustly stabilizes the vehicle over the range of highway speeds (15 to 30 m/s) and a range of expected independent changes in front and rear lateral tire stiffness (15 to 30 kN/rad).