Search

This paper starts from several applications described by initial/boundary value problems for 1D (time and one space variable) hyperbolic partial differential equations whose basic properties and stability of equilibria are studied throughout the same properties for certain associated neutral functional differential equations. It is a common fact that asymptotic stability for neutral functional differential equations is normally obtained under the assumption of asymptotic stability of the difference operator associated to the aforementioned neutral functional differential equations. However the physically meaningful applications presented in the paper have the associated difference operator(s) in critical cases (their stability is, generally speaking, non-asymptotic). Consequently the stability of the considered application models is either non-asymptotic or fragile (in a sense introduced in the paper). The models represent an overview gathered from various fields, processed here in order to emphasize the associated neutral functional differential equations which, consequently, are a challenge to the usual approaches. In the concluding part there are suggested possible ways to overcome these difficulties. [ABSTRACT FROM AUTHOR]

We consider a system of two sets of partial differential equations describing the water hammer in a hydroelectric power plant containing the dynamics of the tunnel, turbine penstock, surge tank and hydraulic turbine. Under standard simplifying assumptions (negligible Darcy-Weisbach losses and dynamic head variations), a system of functional differential equations of neutral type, with two delays, can be associated to the aforementioned partial differential equations and existence, uniqueness and continuous data dependence can be established. Stability is then discussed using a Lyapunov functional deduced from the energy identity. The Lyapunov functional is "weak" i.e. its derivative function is only non-positive definite. Therefore only Lyapunov stability is obtained while for asymptotic stability application of the Barbashin-Krasovskii-LaSalle invariance principle is required. A necessary condition for its validity is the asymptotic stability of the difference operator associated to the neutral system. However, its properties in the given case make the asymptotic stability non-robust (fragile) in function of some arithmetic properties of the delay ratio. [ABSTRACT FROM AUTHOR]

The paper considers a model of co-generation with distributed parameters, described by a non-standard boundary value problem with nonlinear boundary conditions with respect to a system of conservation laws. For the aforementioned model, well posedness in the sense of Hadamard, existence of some invariant sets, equilibria and their stability will be studied. The stabilising feedback laws are synthesised using a suitably constructed Lyapunov functional. [ABSTRACT FROM AUTHOR]

The present paper starts from a model with distributed parameters (i.e. described by hyperbolic partial differential equations with non-standard (derivative) boundary conditions) of a hydroelectric power plant with tunnel, surge tank and penstock. The association of a system of functional differential equations of neutral type and the one-to-one correspondence between the solutions of the two mathematical objects is given. Further, it is given the deduction - via singular pertur-bations - of the nonlinear ordinary differential equations for modeling the surge tank in order to discuss its stability under constant power delivery of the hydraulic turbine. Some other unsolved problems are pointed out. [ABSTRACT FROM AUTHOR]

This volume is dedicated to the 70th anniversary of Vasile Drăgan, an internationally recognized researcher in the area of system and control theory. The impressive scientific results of Vasile Dragan are the output of a life-time sustained work and his special talent for Mathematics. This is a story of "A Beautiful Mind". On this occasion, his collaborators and his colleagues wish him long life in good health and happiness, and more achievements in the field of science. [ABSTRACT FROM AUTHOR]

The paper considers the standard nuclear reactor model with pointwise active zone dynamics together with the dynamics of the external circuits of the reactor in the linearised version. There are presented some Lyapunov functions and the corresponding stability theorems. These Lyapunov functions can be used in synthesising feedback controllers for the reactor power. Two cases - the control Lyapunov function and the sliding mode control - are considered. It is shown that the same Lyapunov functions used in synthesis can be used to obtain stability of the closed-loop reactor-controller. [ABSTRACT FROM AUTHOR]

The paper is concerned with a class of time-delay systems that are linearly equivalent to higher-order scalar equations. If the retarded case was considered some four decades ago in Halanay (1969), the non-trivial neutral case is considered here. The specific structure of these systems endows them with remarkable properties that are useful in various applications in dynamics and control. As an auxiliary necessary result, the variation of parameters formula is revisited what opens new perspectives for research progress in such directions as the Perron condition and forced linear oscillations. [ABSTRACT FROM PUBLISHER]

The main purpose of the paper is to give discrete-time counterpart for some strong (robust) stability results concerning periodic linear Hamiltonian systems. In the continuous-time version, these results go back to Liapunov and Žukovskii; their deep generalizations are due to Kreĭn, Gel'fand, and Jakubovič and obtaining the discrete version is not an easy task since not all results migrate mutatis-mutandis from continuous time to discrete time, that is, from ordinary differential to difference equations. Throughout the paper, the theory of the stability zones is performed for scalar (2nd-order) canonical systems. Using the characteristic function, the study of the stability zones is made in connection with the characteristic numbers of the periodic and skew-periodic boundary value problems for the canonical system. The multiplier motion ("traffic") on the unit circle of the complex plane is analyzed and, in the same context, the Liapunov estimate for the central zone is given in the discrete-time case. [ABSTRACT FROM AUTHOR]

This paper focuses on Forced oscillations (periodic and almost periodic) in some dynamical models described by coupled differential and difference equations. The existence and stability result is based on a theorem on invariant manifolds on Banach spaces due to Kurzweil and Halanay. The state‐space (based on Liapunov–Krasovskii functionals combined with the S‐procedure) approach is considered. An illustrative example is presented and some conclusions are drawn concerning sharpness and ease in applications of the method. [ABSTRACT FROM PUBLISHER]

The article discusses several papers published within the issue including one by A. M. Perdon and M. Anderlucci about disturbance decoupling problem, another by K. Liu, V. Suplin and E. Fridman regarding stability analysis of linear systems and a paper by E. Witrant and colleagues on a model-based feedback control strategy for indoor temperature regulation.