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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]

This work proposes a model predictive control (MPC) approach for a switching linear system where the switching signal is prescribed with unknown future values. The switching signal is known only at its current value, satisfies a minimal dwell-time restriction of $\tau$ steps between successive switchings and is otherwise arbitrary. Under such a setting, the MPC optimization problem has to allow for all admissible switching sequences within a given horizon length. Such a formulation necessitates several other features: the use of a modified returnable set as the terminal constraint; the introduction of consistency constraints on the predicted controls; a min-max optimization criterion as the cost function; the splitting of the horizon into two portions for recursive feasibility consideration and exponential stability of the closed-loop system. The proposed approach is demonstrated by a numerical example. [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]