A wideband active single-sideband time modulator (STM) is proposed in this paper, which achieves high-resolution frequency-independent phase shifting performance through high-precision time delay, eliminating the need for calibrations. The analysis starts with N-step time modulation sequences for the active STM, followed by discussions on enhancing the sideband suppression ratio (SSR) and the effects of quadrature mismatch on SSR. The proposed active STM is based on a periodically controlled active vector modulator with regularly scalable gate-widths, and its timing sequences for control bits feature identical duty cycles and modulation frequency ($f_{\mathrm {P}}$). For verification, a wideband active STM is implemented using 0.13-$\mu $m CMOS technology, which is composed of an input balun and quadrature generator, a periodically controlled 4-bit active vector modulator and a variable-gain stage. Measurement results indicate root mean square (RMS) phase and gain errors ranging from 0.1 to 0.4° and less than 0.2 dB respectively, within a 3-dB frequency range of 13.0 to 20.6 GHz at the maximum gain state. The active STM provides a peak gain of −0.1 dB, an equivalent 10-bit phase control across a 360° range, and a 3-bit gain control spanning 21.0 dB. The measured SSR is below −23.3 dBc, and the instantaneous bandwidth is expanded to$16f_{\mathrm {P}}$. Additionally, the input 1-dB compression point (IP$_{\mathrm {1dB}}$) ranges from 6.1 to 9.3 dBm. The chip occupies a 2.4 mm2 area and consumes 58.8 mW from a 1.2 V supply voltage.

To evaluate the energy-saving effect of the controller, obtaining upper bounds on energy consumption and control time has become a worthwhile and meaningful issue to study. This article mainly discusses three contents about the Kuramoto oscillator network, including fixed-time synchronization (FxTS), prescribed-time synchronization (PTS), and energy consumption estimation. First, to reach FxTS, two sufficient conditions are proposed to guarantee that the Kuramoto oscillator network can reach fixed-time phase agreement and frequency synchronization. Unlike finite/fixed-time controllers, the prescribed-time controller in this article includes a time-varying function term, which is essential to ensure that the system achieves the prescribed-time phase agreement and frequency synchronization. At the same time, the setting-time for PTS is independent of the system initial values or controller parameters, which expands the application prospects of the system. Then, with limited setting-time as a premise, the energy consumed during the fixed/prescribed-time control process is obtained, which helps to evaluate the working time of the system. Finally, an example of a 5-node network is used to illustrate the effectiveness of FxTS and PTS in Kuramoto-oscillator networks.

In this paper, the exponential stability in mean square for Markovian jumping systems (MJSs) is discussed. A new dynamic model, which involves parameters uncertainties, nonlinearities, and Lévy noises, is proposed. Moreover, an adaptive sliding mode controller is built to study the stability of such a complex model. First, an integral-type sliding mode surface (SMS) is established to obtain the sliding mode motion dynamics of MJSs. By the generalized Itô formula and the Lyapunov stability theory, some sufficient conditions are obtained to make sure the exponential stability in mean square for the sliding mode motion dynamics. Second, an adaptive sliding mode control law is provided to assure the reachability of the specified SMS. Furthermore, corresponding parameters of the sliding mode controller and the SMS can be got by solving the convex optimization problem. Finally, the validity of the stability results obtained is illustrated by a numerical simulation and a practical simulation.