Stability properties of a class of sampled regulators with sector bounded nonlinear systems

Recently proposed methods for the design of sampled regulators for unknown linear time invariant systems are considered. It is shown that the regulators satisfy sufficient conditions which guarantee stability when the linear plant is in series with a sector bounded nonlinear, and possibly time varying, element. Furthermore, a simple modification to the methods proposed permits the design of regulators to guarantee closed loop stability when the nonlinear characteristic is in the sector (ε, M) for arbitrarily small ε > 0 and any M > 0.     

Functional integration in CAD systems

This paper examines the issue of integration in CAD systems and argues that for integration to be effective, it must address the functional aspects of a CAD system. It discusses the need for integrated systems and, within a structural engineering context, identifies several facets of integration that should be targeted. These include 2-D drafting and 3-D modelling, graphical and nongraphical design information, the CAD data structure and its user interface, as well as integration of the drafting function with other engineering applications. Means of achieving these levels of integration are briefly discussed and a prognosis for the future development of integrated systems explored. Particular attention is paid to the emergence (and potential role) of ‘product models’ which seek to encapsulate the full range of data elements required to define completely an engineering artefact.     

Direct martingale arguments for stability: The M|G|1 case

A direct martingale argument is given for studying stability properties of the simple M|G|1 queueing system. The technique is of independent interest and can be used elsewhere.     

Data structures and DBMS for computer-aided design systems

The structures for the storage of data in CAD systems influence to a large extent the effectiveness of the system. This paper reviews the wide range of data structures and database management systems (DBMS) available for structuring CAD data. Examples of basic data types are drawn from the MODULA-2 language. The relationship between these basic data types, their composite structures and the classical data models (on which many DBMS are based) is discussed, and the limitations of existing DBMS in modelling CAD data highlighted. A set of requirements for CAD database management systems is drawn up and the emerging role of product models (which seek to encapsulate the totality of data elements required to define fully an engineering artefact) is explored.     

Analysis of dynamic voltage collapse mechanism for a three-bus power system

The phenomenon of voltage collapse is reconstructed based on a three-bus power system with dynamic on-load tap-changers (OLTC). Utilizing nonlinear stability techniques, the monotonic fall of bus voltages is derived from instability of the dynamic system. The exact stability region of the system is constructed which demonstrates the concept of voltage stability region as a tool for the prevention of voltage collapse.     

Global controllability of linear autonomous systems: A geometric consideration

The global controllability in finite time of a linear autonomous system with restrained controls is investigated. Necessary and sufficient conditions are obtained by an approach based on the consideration of geometric properties of the system.     

On the robustness of symmetric systems

This note concerns the robustness of LTI symmetric systems under symmetric or diagonal perturbations. It is shown that for symmetric systems the robust stability condition for dynamic perturbations given by the small gain theorem is also necessary if the perturbation matrix is assumed to be diagonal, but the robust stability condition for parametric perturbations given by the real stability radius is no longer necessary if the perturbation matrix is merely assumed to be symmetric.     

Stabilization of linear systems in the presence of output measurement saturation

This note considers siso nonlinear systems, which have a linear controllable and observable part followed by a measurement saturation nonlinearity. A controller is presented, which feeds back only the saturating output measurements and nevertheless globally asymptotically stabilizes the system. The equilibrium is actually reached in finite time, i.e. the controller is dead beat.     

Stability theory for nonnegative and compartmental dynamical systems with time delay

Nonnegative and compartmental dynamical system models are derived from mass and energy balance considerations and involve the exchange of nonnegative quantities between subsystems or compartments. These models are widespread in biological and physical sciences and play a key role in understanding these processes. A key physical limitation of such systems is that transfers between compartments is not instantaneous and realistic models for capturing the dynamics of such systems should account for material in transit between compartments. In this paper, we present necessary and sufficient conditions for stability of nonnegative and compartmental dynamical systems with time delay. Specifically, asymptotic stability conditions for linear and nonlinear nonnegative dynamical systems with time delay are established using linear Lyapunov–Krasovskii functionals.     

A simple approach for stability margin of discrete systems

In this paper, a technique is presented to determine the stability margin of the discrete systems using recursive algorithm for power of companion matrix and Gerschgorin Theorem and hence sufficient condition of stability is obtained. The method is illustrated with an example and it is compared with other methods proposed in the literature. The results have applications in the filter design.     

On spectral controllability of multi-input time-delay systems

It is proved that under certain verifiable conditions, spectral controllability of a linear system with commensurate state delays and with m inputs, m > 1, implies the existence of an n × 1 vector b contained in the image of the control matrix B such that the system with B replaced by b is spectrally controllable. Both the necessity and the sufficiency of these conditions are shown, a procedure to construct b is given, and an example is discussed.     

Local controllability of nonlinear systems

The local controllability of control systems with an arbitrary number of controls is considered, first on an open set and then at a given point; necessary conditions are derived concerning the Lie algebra T′ generated by the input vector fields, and applied to gradient systems.The main results are a geometric sufficient condition for local controllability at a point, and an equivalent condition based on the computation of Lie brackets, assuming T′ to be (n − 1)-dimensional.     

Anti-windup design with guaranteed regions of stability for discrete-time linear systems

The purpose of this paper is to study the determination of stability regions for discrete-time linear systems with saturating controls through anti-windup schemes. Considering that a linear dynamic output feedback has been designed to stabilize the linear discrete-time system (without saturation), a method is proposed for designing an anti-windup gain that maximizes an estimate of the basin of attraction of the closed-loop system in the presence of saturation. It is shown that the closed-loop system obtained from the controller plus the anti-windup gain can be locally modeled by a linear system with a deadzone nonlinearity. Then, based on the use of a new sector condition and quadratic Lyapunov functions, stability conditions in an LMI form are stated. These conditions are then considered in a convex optimization problem in order to compute an anti-windup gain that maximizes an estimate of the basin of attraction of the closed-loop system. Moreover, considering asymptotically stable open-loop systems, it is shown that the conditions can be slightly modified in order to determine an anti-windup gain that ensures global stability. An extension of the proposed results to the case of dynamic anti-windup synthesis is also presented in the paper.     

Bisimilar control affine systems

The notion of bisimulation plays a very important role in theoretical computer science where it provides several notions of equivalence between models of computation. These equivalences are in turn used to simplify verification and synthesis for these models as well as to enable compositional reasoning. In systems theory, a similar notion is also of interest in order to develop modular verification and design tools for purely continuous or hybrid control systems. In this paper, we introduce two notions of bisimulation for nonlinear systems. We present differential geometric characterizations of these notions and show that bisimilar systems of different dimensions are obtained by factoring out certain invariant distributions. Furthermore, we also show that all bisimilar systems of different dimension are of this form.     

Nonparametric identification of quasi-stationary systems

Recursive estimates of a regression function — based on the Parzen-Rosenblatt kernels — are applied for identification of quasi-stationary systems. It is shown that these estimates do not lose their asymptotic properties even if the data are not stationary. Conditions for weak and strong pointwise consistency are given.     

Exit problem and control theory

The first part of the paper is concerned with a version of Freidlin-Wentzell exit theorems suitable for control theoretic applications. In the second part the general results are specialized to the case of linear systems and two types of stabilizability questions are considered.     

On stability of linear all-pass systems

In this paper we analyze the class of all-pass, linear and stable systems. We give a condition on the zero distribution of the transfer function of such a system to guarantee stability and we show that stability is not preserved under cascade decomposition.     

Necessary and sufficient conditions for quadratic controllability of a class of uncertain systems

We introduce a controllability notion for uncertain systems, namely, quadratic controllability. For a specific class of norm bounded uncertain systems, we show that this notion is equivalent to controllability of a nominal system and the satisfaction of a certain structural condition by the uncertainty. For systems in which the uncertain parameters affect all control inputs, this structural condition is simply the familiar matching condition commonly encountered in the literature on robust and adaptive control of uncertain systems.