Introduction to linear and nonlinear programming

Feedback systems: Input-output properties

Zames-Falb multipliers for absolute stability: from O'Shea's contribution to convex searches

Second-order counterexamples to the discrete-time Kalman conjecture

Equivalence between classes of multipliers for slope-restricted nonlinearities

The formula for stability multipliers for systems with MIMO nonlinearities is derived using the method of delay-integral-quadratic constraints. The results, applicable to both time-invariant and time-periodic systems, are then used to derive a solution for a special case of a nonlinear regulation problem and a criterion for stability of forced oscillations. A linear time-periodic system is considered to illustrate the difference between the delay-integral-quadratic constraints that yield stability criteria in multiplier form and those that do not.

Delay-Integral-Quadratic Constraints and Stability Multipliers for Systems With MIMO Nonlinearities

Frequency Domain Criteria for Absolute Stability: A Delay-integral-quadratic Constraints Approach

Frequency Domain Criteria for Absolute Stability

Aquatic nuisance species (ANS) in ship's ballast water are killed by permeating to equilibrium a gaseous mixture consisting essentially of, preferably, ≧84% nitrogen, ≧11% carbon dioxide and ≦4% oxygen through ship's ballast water until the ballast water itself becomes (i) hypercapnic to ≧20 ppm carbon dioxide, and, by association, (ii) acidic to pH≦7, while preferably further, and also, being rendered (iii) hypoxic to ≦1 ppm oxygen. The permeating is preferably realized by bubbling the gaseous mixture preferably obtained from an inert gas generator through the ballast water over the course of 2+ days while the ballast water is continually maintained a pressure less than atmosphere, preferably −2 p.s.i. or less. The (i) hypercapnic, (ii) acidic and (iii) hypoxic conditions—each of which can be independently realized—synergistically cooperate to kill a broad range of ANS in the ballast water without deleterious effect on the environment when, and if, the ballast water in which the balance of dissolved gases has been changed is discharged.

Infusion of combustion gases into ballast water preferably under less than atmospheric pressure to synergistically kill harmful aquatic nuisance species by simultaneous hypercapnia, hypoxia and acidic pH level

This paper considers the Aizerman problem for second-order systems with delays. It is proved that for retarded systems with a single delay the Aizerman conjecture is true. For systems with multiple delays, a delay-dependent class of systems is found, for which the Aizerman conjecture is true. The proof is based on the Popov's frequency-domain criterion for absolute stability.

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Dmitry Altshuller

Papers

Delay-Integral-Quadratic Constraints and Stability Multipliers for Systems With MIMO Nonlinearities

Frequency Domain Criteria for Absolute Stability: A Delay-integral-quadratic Constraints Approach

Frequency Domain Criteria for Absolute Stability

Infusion of combustion gases into ballast water preferably under less than atmospheric pressure to synergistically kill harmful aquatic nuisance species by simultaneous hypercapnia, hypoxia and acidic pH level

A Partial Solution of the Aizerman Problem for Second-Order Systems With Delays