Dissipative Stabilization of Linear Systems with Time-Varying General Distributed Delays (Complete Version)

New methods are developed for the stabilization of a linear system with general time-varying distributed delays existing at the system's states, inputs and outputs. In contrast to most existing literature where the function of time-varying delay is continuous and bounded, we assume it to be bounded and measurable. Furthermore, the distributed delay kernels can be any square-integrable function over a bounded interval, where the kernels are handled directly by using a decomposition scenario without using approximations. By constructing a Krasovski\u{i} functional via the application of a novel integral inequality, sufficient conditions for the existence of a dissipative state feedback controller are derived in terms of matrix inequalities without utilizing the existing reciprocally convex combination lemmas. The proposed synthesis (stability) conditions, which take dissipativity into account, can be either solved directly by a standard numerical solver of semidefinite programming if they are convex, or reshaped into linear matrix inequalities, or solved via a proposed iterative algorithm. To the best of our knowledge, no existing methods can handle the synthesis problem investigated in this paper. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed methodologies.Comment: Accepted by Automatic

Robust <i>H</i>_&#x221e; Fuzzy Control Design for Nonlinear Two-Time Scale System with Markovian Jumps based on LMI Approach

Non

Fuzzy H-infinity output feedback control of nonlinear systems under sampled measurements

This paper studies the problem of designing an H∞ fuzzy feedback control for a class of nonlinear systems described by a continuous-time fuzzy system model under sampled output measurements. The premise variables of the fuzzy system model are allowed to be unavailable. We develop a technique for designing an H∞ fuzzy feedback control that guarantees the L2 gain from an exogenous input to a controlled output is less than or equal to a prescribed value. A design algorithm for constructing the H∞ fuzzy feedback controller is given

Integral Inequalities for the Analysis of Distributed Parameter Systems: A complete characterization via the Least-Squares Principle

A wide variety of integral inequalities (IIs) have been proposed and studied for the stability analysis of distributed parameter systems using the Lyapunov functional approach. However, no unified mathematical framework has been proposed that could characterize the similarity and connection between these IIs, as most of them was introduced in a dispersed manner for the analysis of specific types of systems. Additionally, the extent to which the generality of these IIs can be expanded and the optimality of their lower bounds (LBs) remains open questions. In this work, we present two general classes of IIs that can generalize almost all IIs in the literature, whose integral kernels can contain a unlimited number of weighted L2 functions that are linearly independent in a Lebesgue sense. Moreover, we not only demonstrate the equivalence between the LBs of the proposed IIs under the same kernels and weighted functions, but also show that these LBs are guaranteed by the least squares principle, implying asymptotic convergence to the upper bound when the kernels functions constitutes a Schauder basis of the underlying Hilbert space. Given their general structures, the proposed IIs can be applied in various situations such as the stability analysis of coupled PDE-ODE systems or cybernetic systems that can be characterized by delay structures.Comment: Submitted to ACC 202

Design Of Capacitive Power Transfer Using A Class-E Resonant Inverter

This paper presents a capacitive power transfer (CPT) system using a Class-E resonant inverter. A Class-E resonant inverter is chosen because of its ability to perform DC-to-AC inversion efficiently while significantly reducing switching losses. The proposed CPT system consists of an efficient Class-E resonant inverter and capacitive coupling formed by two flat rectangular transmitter and receiver plates. To understand CPT behavior, we study the effects of various coupling distances on output power performance. The proposed design is verified through lab experiments with a nominal operating frequency of 1 MHz and 0.25 mm coupling gap. An efficiency of 96.3% is achieved. A simple frequency tracking unit is also proposed to tune the operating frequency in response to changes in the coupling gap. With this resonant frequency tracking unit, the efficiency of the proposed CPT system can be maintained within 96.3%–91% for the coupling gap range of 0.25–2 mm