Simple conditions for sampled-data stabilization by using artificial delay

It is well known that in some systems a stabilizing feedback that depends on the output and its derivative can be replaced by delay-dependent feedback where the derivative is approximated by a finite difference. We study sampled-data implementation of such delay-dependent feedback. The analysis is based on the Taylor representation of the delayed signal with the remainder in the integral form, which is then compensated by appropriate Lyapunov-Krasovskii functional. This allows to obtain simple LMI-based conditions guaranteeing a desired decay rate of convergence. Using these conditions, we prove that if the system can be stabilized by continuous-time derivative-dependent feedback then it can be stabilized by sampled-data delay-dependent feedback with small enough sampling and delay. Finally, we introduce the event-triggering mechanism that allows to reduce the amount of transmitted signals at the cost of larger memory used

An Input-to-State Stability Approach to Verify Almost Global Stability of a Synchronous-Machine-Infinite-Bus System

Conditions for almost global stability of an operating point of a realistic model of a synchronous generator with constant field current connected to an infinite bus are derived. The analysis is conducted by employing the recently proposed concept of input-to-state stability (ISS)–Leonov functions, which is an extension of the powerful cell structure principle developed by Leonov and Noldus to the ISS framework. Compared with the original ideas of Leonov and Noldus, the ISS–Leonov approach has the advantage of providing additional robustness guarantees. The efficiency of the derived sufficient conditions is illustrated via numerical experiments

Theory of differential inclusions and its application in mechanics

The following chapter deals with systems of differential equations with discontinuous right-hand sides. The key question is how to define the solutions of such systems. The most adequate approach is to treat discontinuous systems as systems with multivalued right-hand sides (differential inclusions). In this work three well-known definitions of solution of discontinuous system are considered. We will demonstrate the difference between these definitions and their application to different mechanical problems. Mathematical models of drilling systems with discontinuous friction torque characteristics are considered. Here, opposite to classical Coulomb symmetric friction law, the friction torque characteristic is asymmetrical. Problem of sudden load change is studied. Analytical methods of investigation of systems with such asymmetrical friction based on the use of Lyapunov functions are demonstrated. The Watt governor and Chua system are considered to show different aspects of computer modeling of discontinuous systems

Urinary pH: its regulation and relevance in urolithiasis metaphylaxis

Urolithiasis is a common multifactorial disease characterized by a high recurrence rate. This review is devoted to the urine pH as one of the main factors determining its lithogenic properties. It affects the excretion of lithogenic substances and stone formation inhibitors, the solubility, and the crystallization of substances involved in stone formation. The urine pH significantly affects the solubility of uric acid in urine, which decreases at a pH < 5.5. This explains the high incidence of uric acid concretions in patients with metabolic syndrome. Their insulin resistance leads to a decrease in the excretion of ammonium ions in the proximal tubules, leading to persistent urine acidification. The activity of many transport processes involved in the processing of calcium, citrates and phosphates is sensitive to changes in systemic or local pH. The data on the effect of urine pH on the solubility of calcium oxalate remain contradictory. At the same time, there is no doubt about the determining role of urine pH in the excretion of citrate, the most important stone formation inhibitor. The alkaline urine pH promotes the formation of concretions containing calcium phosphates. In conditions of constantly elevated urine pH in patients with persistent urease-producing urinary tract infection, a rapid growth of "infectious" concretions occurs. The review summarizes information on the causes of the decrease and increase in the urine pH, as well as the possibilities of medicinal and non-medicinal methods of modifying the urine pH during the prevention of stone formation recurrence

A third-order class-D amplifier with and without ripple compensation

We analyse the nonlinear behaviour of a third-order class-D amplifier, and demonstrate the remarkable effectiveness of the recently introduced ripple compensation (RC) technique in reducing the audio distortion of the device. The amplifier converts an input audio signal to a high-frequency train of rectangular pulses, whose widths are modulated according to the input signal (pulse-width modulation) and employs negative feedback. After determining the steady-state operating point for constant input and calculating its stability, we derive a small-signal model (SSM), which yields in closed form the transfer function relating (infinitesimal) input and output disturbances. This SSM shows how the RC technique is able to linearise the small-signal response of the device. We extend this SSM through a fully nonlinear perturbation calculation of the dynamics of the amplifier, based on the disparity in time scales between the pulse train and the audio signal. We obtain the nonlinear response of the amplifier to a general audio signal, avoiding the linearisation inherent in the SSM; we thereby more precisely quantify the reduction in distortion achieved through RC. Finally, simulations corroborate our theoretical predictions and illustrate the dramatic deterioration in performance that occurs when the amplifier is operated in an unstable regime. The perturbation calculation is rather general, and may be adapted to quantify the way in which other nonlinear negative-feedback pulse-modulated devices track a time-varying input signal that slowly modulates the system parameters

Absolute stability of time-varying delay Lurie indirect control systems with unbounded coefficients

This paper investigates the absolute stability problem of time-varying delay Lurie indirect control systems with variable coefficients. A positive-definite Lyapunov-Krasovskii functional is constructed. Some novel sufficient conditions for absolute stability of Lurie systems with single nonlinearity are obtained by estimating the negative upper bound on its total time derivative. Furthermore, the results are generalised to multiple nonlinearities. The derived criteria are especially suitable for time-varying delay Lurie indirect control systems with unbounded coefficients. The effectiveness of the proposed results is illustrated using simulation examples

Survey on time-delay approach to networked control

This paper provides a survey on time-delay approach to networked control systems (NCSs). The survey begins from a brief summary on fundamental network-induced issues in NCSs and the main approaches to the modelling of NCSs. In particular, a comprehensive introduction to time-delay approach to sampled-data and networked control is provided. Then, recent results on time-delay approach to event-triggered control are recalled. The survey highlights time-delay approach developed to modelling, analysis and synthesis of NCSs, under communication constraints, with a particular focus on Round-Robin, Try-once-discard and stochastic protocols. The time-delay approach allows communication delays to be larger than the sampling intervals in the presence of scheduling protocols. Moreover, some results on networked control of distributed parameter systems are surveyed. Finally, conclusions and some future research directions are briefly addressed