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This paper examines the problem of stabilizing linear distributed delay systems with nonlinear distributed delay kernels and dissipativity constraints. Specifically, the nonlinear distributed kernel includes functions such as polynomials, trigonometric and exponential functions. By constructing a Liapunov-Krasovski\v{i} functional related to the distributed kernels, sufficient conditions for the existence of a state feedback controller which stabilizes the uncertain distributed delay systems with dissipativity constraints are given in terms of linear matrix inequalities (LMIs). In contrast to existing methods, the proposed scenario is less conservative or requires a smaller number of decision variables based on the application of a newly derived integral inequality. Finally, numerical examples are presented to demonstrate the validity and effectiveness of the proposed methodology., Comment: https://doi.org/10.1016/j.sysconle.2016.06.017. arXiv admin note: text overlap with arXiv:2204.08353

A wide variety of integral inequalities (IIs) have been developed 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 study, we introduce two general classes of IIs that can generalize nearly all IIs in the literature. The integral kernels of the LBs of our IIs can contain an unlimited number of weighted $\mathcal{L}^2$ functions that are linearly independent in a Lebesgue sense. Moreover, we not only establish the equivalence relations between the LBs of our IIs, but also demonstrate 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. Owing to their general structures, our IIs are applicable in a variety of contexts, such as the stability analysis of coupled PDE-ODE systems or cybernetic systems with delay structures., Comment: To be presented at ACC 2024

This book is an extension of my doctoral dissertation, focusing on techniques for analyzing stability (dissipativity) and achieving stabilization of linear systems that are characterized by non-trivial distributed delays. It specifically explores the application of the Lyapunov-Krasovskii functional (LKF) approach., Comment: The material will receive regular updates to maintain the book's status as a thorough and up-to-date reference for research into systems with distributed delays

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: The work is the full version of the paper https://doi.org/10.1016/j.automatica.2020.109227

In this note, we present two general classes of integral inequalities motivated by their applications to infinite dimensional systems. The inequalities possess general structures in terms of weight functions and lower quadratic bounds. Many existing inequalities in the published literature, including those with free matrix variables, are the special cases of our inequalities. An relation on the lower bounds of the proposed inequalities is also established. For specific applications, our inequalities are applied to construct a Liapunov-Krasovskii functional for the stability analysis of a linear coupled differential-difference system with a distributed delay, which gives to equivalent stability conditions based on the properties of the proposed inequalities. Finally, it is worthy to note that the inequalities in this note can be applied in general contexts such as the stability analysis of PDE-related systems or sampled-data systems.

This paper proposes methods to handle the problem of delay range stability analysis for a linear coupled differential-difference system (CDDS) with distributed delays subject to dissipative constraints. The model of linear CDDS contains many models of linear delay systems as special cases. A novel Liapunov-Krasovskii functional with non-constant matrix parameters, which are related to the delay value polynomially, is applied to derive stability conditions. By constructing this new functional, sufficient conditions in terms of robust linear matrix inequalities (LMIs) can be derived, which guarantee range stability of a linear CDDS subject to dissipative constraints. To solve the resulting robust LMIs numerically, we apply the technique of sum of squares programming together with matrix relaxations without introducing any potential conservatism to the original robust LMIs. Furthermore, the proposed methods can be extended to solve delay margin estimation problems for a linear CDDS subject to prescribed dissipative constraints. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed methodologies.

In this paper, we present a new method for the dissipativity and stability analysis of a linear coupled differential-difference system (CDDS) with general distributed delays at both state and output. More precisely, the distributed delay terms under consideration can contain any $\fL^{2}$ functions which are approximated via a class of elementary functions which includes the option of Legendre polynomials. By using this broader class of functions compared to the existing Legendre polynomials approximation approach, one can construct a Liapunov-Krasovskii functional which is parameterized by non-polynomial functions . Furthermore, a novel generalized integral inequality is also proposed to incorporate approximation error in our stability (dissipativity) conditions. Based on the proposed approximation scenario with the proposed integral inequality, sufficient conditions determining the dissipativity and stability of a CDDS are derived in terms of linear matrix inequalities. In addition, several hierarchies in terms of the feasibility of the proposed conditions are derived under certain constraints. Finally, several numerical examples are presented in this paper to show the effectiveness of our proposed methodologies., Comment: A paper containing a simplified one delay version of the dissipative stability analysis method of this paper has been submitted to IEEE Transactions on Automatic Control

This paper develops a novel power harvesting system to harvest ambient RF energy to power a wireless sensor. Harvesting ambient RF energy is a very difficult task as the power levels are extremely weak. Simulation results show zero threshold MOSFETs are essential in the RF to DC conversion process. 0.5VDC at the output of the RF to DC conversion stage is the minimum voltage which must be achieved for the micro-power sensor circuitry to operate. The weakest power level the proposed system can successfully harvest is -37dBm. The measured available power from the FM band has been measured to fluctuate between -33 to -43dBm using a ribbon FM dipole antenna. Ambient RF energy would best be used in conjunction with other forms of harvested ambient energy to increase diversity and dependability. The potential economic and environmental benefits make such endeavors truly worthwhile.