Stability of differential-difference equations representing heat exchanger and certain other systems†

Conditions for the stability of certain typos of first-order nonlinear difTerential-difforonce equations are derived. Some of the results are applicable to a simplified model of certain distributed parameter systems, such as heat exchanger.     

A note on attraction and stability of neutral stochastic delay differential equations with Markovian switching

This paper is concerned with neutral stochastic delay differential equations with Markovian switching (NSDDEs-MS). A kind of ψ ??function is introduced and some criteria on the attractor for the product of the ψ ??function are obtained. By the new criteria, the almost sure stability with the general decay rate of NSDDEs-MS could be examined, including the exponential stability and the polynomial stability. Finally, an example is provided to illustrate the applications of our results clearly.     

Orthonormal basis functions applied to optimal control design with closed-loop pole location constraints

This article proposes an optimal control design technique to ensure that the closed-loop poles are assigned to prescribed locations in the complex plane. A key element in this approach is the usage of orthonormal basis functions to parametrise the main design parameter. This goal is achieved by using a quadratic cost based optimisation approach, considering control effort penalisation as well as cheap control. Youla parametrisation is used, subject to a set of constraints which guarantee stability, zero steady error to constant references and disturbances, and yielding the prescribed set of closed-loop poles.