Robust State Feedback for Interval Systems: An Interval Analysis Approach

The problem of robust state feedback design for a linear dynamical system with uncertain (interval) parameters is considered. The designed state feedback controller has to place all the coefficients of the closed loop system characteristic polynomial within assigned closed loop interval characteristic polynomial. A condition is derived using certain known facts about matrix minors and its characteristic equation. The derived condition assigns the closed loop coefficients of the system characteristic polynomial within the assigned closed loop interval polynomial, if certain inequalities admit a positive solution. The method is simple and has advantage that it does not require system canonical transformation. The efficacy of the method is illustrated using numerical examples.