New Control Design for Switched Linear Time-Invariant Systems under Arbitrary Switching

This paper proposes a new design procedure for a class of switched linear time-invariant (LTI) systems based on the so called "common zeroing output system" technique. Only relying on the existence of a common weak Lyapunov function, a family of controllers can be designed to achieve uniform global exponential stability (UGES) for arbitrarily switched systems. Two illustrative examples illustrate that the proposed scheme can be used to ensure UGES even though finding a common quadratic strict Lyapunov function is sometimes impossible for arbitrarily switched LTI systems.