Robust control of switched linear systems

We consider robust control of switched linear systems under arbitrary time-dependent switching signals. First, we introduce a common quadratic Lyapunov function for the class of switched linear systems with Hurwitz constituent matrices in ℝ^n×n sharing n - 1 linearly independent common left eigenvectors. The common quadratic Lyapunov function is then used for robust stability analysis of the convexified differential inclusion associated with the underlying switched linear system. Finally, using the common left eigenstructure assignment approach for multi-input systems, robust design by means of state-feedback control is proposed.