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We study feedback control for a discrete-time integrator with unitary delay in the presence of quantization both in the control action and in the measurement of the controlled variable. In some applications the quantization effects can be neglected, but when high precision is needed, they have to be explicitly accounted for in control design. In this paper, we propose a switched control solution for minimizing the effect of quantization of both the control and controlled variables for the considered system, that is quite common in the computing systems domain, for example, in thread scheduling, clock synchronization, and resource allocation. We show that the switched solution outperforms the one without switching, designed by neglecting quantization, and analyze necessary and sufficient conditions for the controlled system to exhibit periodic solutions in the presence of an additive constant disturbance affecting the control input. Simulation results provide evidence of the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

This paper introduces the notion of common zeroing-output systems (CZOS) to analyze the stability of switched systems. The concept of CZOS allows one to verify weak zero-state detectability. It characterizes a common behavior of any individual subsystem when the output signal for each subsystem is “approaching” zero. Heuristically speaking, it removes the effect of switching behavior, and thus enables one to analyze stability properties in systems with complex switching signals. With the help of CZOS, the Krasovskii–LaSalle theorem can be extended to switched nonlinear time-varying systems with both arbitrary switching and more general restricted switching cases. For switched nonlinear time-invariant systems, the needed detectability condition is further simplified, leading to several new stability results. Particularly, when a switched linear time-invariant system is considered, it is possible to generate a recursive method, which combines a Krasovskii–LaSalle result and a nested Matrosov result, to find a CZOS if it exists. The power of the proposed CZOS is demonstrated by consensus problems in literature to obtain a stronger convergence result with weaker conditions. [ABSTRACT FROM AUTHOR]