Computation of Zeros of Linear Multivariable Systems

Several algorithms have been proposed in the literature for the computation of the zeros of a linear system described by a state-space model {A, B, C, D}. In this paper we discuss the numerical properties of a new algorithm and compare it with some earlier techniques of computing zeros. The method is a modified version of Silverman's structure algorithm and is shown to be backward stable in a rigorous sense. The approach is shown to handle both nonsquare and/or degenerate systems. Several numerical examples are also provided

A Unifying Framework for Finite Wordlength Realizations.

A general framework for the analysis of the finite wordlength (FWL) effects of linear time-invariant digital filter implementations is proposed. By means of a special implicit system description, all realization forms can be described. An algebraic characterization of the equivalent classes is provided, which enables a search for realizations that minimize the FWL effects to be made. Two suitable FWL coefficient sensitivity measures are proposed for use within the framework, these being a transfer function sensitivity measure and a pole sensitivity measure. An illustrative example is presented

Orientation of Implicit State Space Models and the Partitioning of Kronecker Structure

Early stages modelling of processes involves issues of classification of variables into inputs, outputs and internal variables, referred to as Model Orientation Problem (MOP) which may be addressed on state space implicit, or matrix pencil descriptions. Defining orientation is equivalent to producing state space models of the regular or singular type. In this paper we consider autonomous differential descriptions defined by matrix pencils and then search for strict equivalence transformations which introduce the partitioning of the implicit vector into states and possible inputs and outputs, referred to as system orientation. The Kronecker invariant structure of the matrix pencil description is shown to be central to the solution of system orientation and this is expressed as a problem of classification and partitioning of the Kronecker invariants. It is shown that the types of Kronecker invariants characterise the nature of the system orientation solutions. Studying the conditions, under which such oriented models may be derived, as well as their structural properties in terms of the Kronecker structure, is the issue considered here

Finite-region stability of 2-D singular Roesser systems with directional delays

In this paper, the problem of finite-region stability is studied for a class of two-dimensional (2-D) singular systems described by using the Roesser model with directional delays. Based on the regularity, we first decompose the underlying singular 2-D systems into fast and slow subsystems corresponding to dynamic and algebraic parts. Then, with the Lyapunov-like 2-D functional method, we construct a weighted 2-D functional candidate and utilize zero-type free matrix equations to derive delay-dependent stability conditions in terms of linear matrix inequalities (LMIs). More specifically, the derived conditions ensure that all state trajectories of the system do not exceed a prescribed threshold over a pre-specified finite region of time for any initial state sequences when energy-norms of dynamic parts do not exceed given bounds

A pulse size estimation method for reduced-order models

Model-Order Reduction (MOR) is an important technique that allows Reduced-Order Models (ROMs) of physical systems to be generated that can capture the dominant dynamics, but at lower cost than the full order system. One approach to MOR that has been successfully implemented in fluid dynamics is the Eigensystem Realization Algorithm (ERA). This method requires only minimal changes to the inputs and outputs of a CFD code so that the linear responses of the system to unit impulses on each input channel can be extracted. One of the challenges with the method is to specify the size of the input pulse. An inappropriate size may cause a failure of the code to converge due to non-physical behaviour arising during the solution process. This paper addresses this issue by using piston theory to estimate the appropriate input pulse size

Robust stabilization of singular-impulsive-delayed systems with nonlinear perturbations

Many dynamic systems in physics, chemistry, biology, engineering, and information science have impulsive dynamical behaviors due to abrupt jumps at certain instants during the dynamical process, and these complex dynamic behaviors can be modeled by singular impulsive differential systems. This paper formulates and studies a model for singular impulsive delayed systems with uncertainty from nonlinear perturbations. Several fundamental issues such as global exponential robust stabilization of such systems are established. A simple approach to the design of a robust impulsive controller is then presented. A numerical example is given for illustration of the theoretical results. Meanwhile, some new results and refined properties associated with the M-matrices and time-delay dynamic systems are derived and discussed.published_or_final_versio