Improved Stability Conditions for Switched Linear Time‐Varying Systems Based on Matrix Structural Decomposition

ABSTRACT This manuscript considers the problem of uniform asymptotic stability (UAS) for switched linear time‐varying (SLTV) systems. First, an estimate of the eigenvalues of time‐varying matrices is given by using the mixed norms of matrices. Also, a UAS condition of systems is proposed by using the uniform divergence property of infinite integrals. Second, based on the structural decomposition of the time‐varying matrix of systems, two improved stability conditions are given to verify the UAS of the system under any switching, and a switching signal is designed in the presence of unstable subsystems. Compared with existing results, the obtained results relax the constraints on the time‐varying matrix of systems, and ensure that the system is UAS, not just (globally) asymptotically stable. Finally, a numerical example is provided to illustrate the theoretical results.