This paper studies a number of quantized feedback design problems for linear systems. We consider the case where quantizers are static (memoryless). The common aim of these design problems is to stabilize the given system or to achieve certain performance with the coarsest quantization density. Our main discovery is that the classical sector bound approach is nonconservative for studying these design problems. Consequently, we are able to convert many quantized feedback design problems to well-known robust control problems with sector bound uncertainties. In particular, we derive the coarsest quantization densities for stabilization for multiple-input-multiple-output systems in both state feedback and output feedback cases; and we also derive conditions for quantized feedback control for quadratic cost and H/sub /spl infin// performances.

The sector bound approach to quantized feedback control | NOVA. The University of Newcastle's Digital Repository

The free-weighting matrix and integral-inequality methods are widely used to derive delay-dependent criteria for the stability analysis of time-varying-delay systems because they avoid both the use of a model transformation and the technique of bounding cross terms. This technical note presents a new integral inequality, called a free-matrix-based integral inequality, that further reduces the conservativeness in those methods. It includes well-known integral inequalities as special cases. Using it to investigate the stability of systems with time-varying delays yields less conservative delay-dependent stability criteria, which are given in terms of linear matrix inequalities. Two numerical examples demonstrate the effectiveness and superiority of the method.

Free-Matrix-Based Integral Inequality for Stability Analysis of Systems With Time-Varying Delay

A recent set of overused population-based methods have been published in recent years. Despite their popularity, most of them have uncertain, immature performance, partially done verifications, similar overused metaphors, similar immature exploration and exploitation components and operations, and an insecure tradeoff between exploration and exploitation trends in most of the new real-world cases. Therefore, all users need to extensively modify and adjust their operations based on main evolutionary methods to reach faster convergence, more stable balance, and high-quality results. To move the optimization community one step ahead toward more focus on performance rather than change of metaphor, a general-purpose population-based optimization technique called Hunger Games Search (HGS) is proposed in this research with a simple structure, special stability features and very competitive performance to realize the solutions of both constrained and unconstrained problems more effectively. The proposed HGS is designed according to the hunger-driven activities and behavioural choice of animals. This dynamic, fitness-wise search method follows a simple concept of “Hunger” as the most crucial homeostatic motivation and reason for behaviours, decisions, and actions in the life of all animals to make the process of optimization more understandable and consistent for new users and decision-makers. The Hunger Games Search incorporates the concept of hunger into the feature process; in other words, an adaptive weight based on the concept of hunger is designed and employed to simulate the effect of hunger on each search step. It follows the computationally logical rules (games) utilized by almost all animals and these rival activities and games are often adaptive evolutionary by securing higher chances of survival and food acquisition. This method's main feature is its dynamic nature, simple structure, and high performance in terms of convergence and acceptable quality of solutions, proving to be more efficient than the current optimization methods. The effectiveness of HGS was verified by comparing HGS with a comprehensive set of popular and advanced algorithms on 23 well-known optimization functions and the IEEE CEC 2014 benchmark test suite. Also, the HGS was applied to several engineering problems to demonstrate its applicability. The results validate the effectiveness of the proposed optimizer compared to popular essential optimizers, several advanced variants of the existing methods, and several CEC winners and powerful differential evolution (DE)-based methods abbreviated as LSHADE, SPS_L_SHADE_EIG, LSHADE_cnEpSi, SHADE, SADE, MPEDE, and JDE methods in handling many single-objective problems. We designed this open-source population-based method to be a standard tool for optimization in different areas of artificial intelligence and machine learning with several new exploratory and exploitative features, high performance, and high optimization capacity. The method is very flexible and scalable to be extended to fit more form of optimization cases in both structural aspects and application sides. This paper's source codes, supplementary files, Latex and office source files, sources of plots, a brief version and pseudocode, and an open-source software toolkit for solving optimization problems with Hunger Games Search and online web service for any question, feedback, suggestion, and idea on HGS algorithm will be available to the public at https://aliasgharheidari.com/HGS.html .

Hunger games search: Visions, conception, implementation, deep analysis, perspectives, and towards performance shifts

Stability problems of continuous-time recurrent neural networks have been extensively studied, and many papers have been published in the literature The purpose of this paper is to provide a comprehensive review of the research on stability of continuous-time recurrent neural networks, including Hopfield neural networks, Cohen-Grossberg neural networks, and related models Since time delay is inevitable in practice, stability results of recurrent neural networks with different classes of time delays are reviewed in detail For the case of delay-dependent stability, the results on how to deal with the constant/variable delay in recurrent neural networks are summarized The relationship among stability results in different forms, such as algebraic inequality forms, \(M\) -matrix forms, linear matrix inequality forms, and Lyapunov diagonal stability forms, is discussed and compared Some necessary and sufficient stability conditions for recurrent neural networks without time delays are also discussed Concluding remarks and future directions of stability analysis of recurrent neural networks are given

https://romisatriawahono.net/lecture/rm/survey/machine%20learning/Zhang%20-%20Stability%20Analysis%20of%20Continuous-Time%20Recurrent%20Neural%20Networks%20-2014.pdf

A Comprehensive Review of Stability Analysis of Continuous-Time Recurrent Neural Networks

In this paper we discussed delay-dependent feedback stabilization of linear uncertain state-delayed systems. Based on the status feedback of system, the control regularity for the feedback stability of system is offered. Using the linear matrix inequality (LMI), we got the sufficient condition for the feedback stability of system. Finally an illustrative example verified the effectiveness and rationality of the conclusion.

Hong-Bing Zeng

Papers

Free-Matrix-Based Integral Inequality for Stability Analysis of Systems With Time-Varying Delay

New results on stability analysis for systems with discrete distributed delay

Stability analysis of systems with time-varying delay via relaxed integral inequalities

A new looped-functional for stability analysis of sampled-data systems

A generalized free-matrix-based integral inequality for stability analysis of time-varying delay systems