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In this note, a novel conception called virtual clock, which is defined by an artificial timer over a finite cycle, is introduced for stability analysis of discrete-time switched linear systems under minimum dwell-time constraint. Two necessary and sufficient conditions associated with a virtual clock with a sufficient length are proposed to ensure the global uniform asymptotic stability of discrete-time switched linear systems. For the two nonconservative stability criteria, the lifted version maintains the convexity in system matrices. Based on the lifted convex conditions, the extensions to $\ell _2$ -gain computation and $\mathcal {H}_\infty$ control problems are presented in the sequel. In particular, a novel virtual-clock-dependent controller is designed, which outperforms the traditional mode-dependent and common gain controllers. Several numerical examples are provided to illustrate our theoretic results. [ABSTRACT FROM AUTHOR]

In this technical note, a necessary and sufficient stability criterion for switched linear systems under dwell-time constraint is proposed by employing a class of time-scheduled homogeneous polynomial Lyapunov functions with a sufficiently large degree. The key feature of this nonconservative condition lies in its convexity in the system matrices, which explicitly facilitates its further extension to uncertain systems. Then, in order to obtain numerically testable condition, a family of LMI conditions are presented with the aid of the idea of dividing the dwell-time interval into a finite number of segments. It is proved that the non-conservativeness can be maintained with a sufficiently large interval dividing parameter. In the end, the result is straightforwardly extended to the uncertain case in virtue of the convexity in the system matrices. Numerical examples are presented to illustrate our findings. [ABSTRACT FROM PUBLISHER]