Search

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 paper investigates standard $H_\infty$ control of switched systems via dwell-time switchings without posing any internal stability requirements on subsystems of the switched systems. First, a sufficient condition is formed by specifying lower and upper bounds of the dwell time, constraining upper bound of derivative of a Lyapunov function of the active subsystem, and forcing the Lyapunov function values of the overall switched system to decrease at switching times to achieve standard $H_\infty$ control of unforced switched linear systems. Then, in the same framework of the dwell time, sufficient conditions are given for that of the corresponding forced switched linear systems by further designing state feedback controllers. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed 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]

This work deals with the problem of rendering the output of a switched linear system insensitive to a disturbance input, with the requirement that the dynamics of the closed-loop system be exponentially stable for all switching signals with a sufficiently large dwell time. A necessary and sufficient condition for the problem to have a solution is shown. A complete computational procedure to check the solvability condition and to synthesize the compensation scheme is provided. A worked-out example is presented with the aim of showing the effectiveness of the devised method. [ABSTRACT FROM AUTHOR]