Further results on controllability and sensitivity

The structural uncontrollability of the sensitivity system is defined relative to a class of linear time-invariant systems. Previously obtained results are reviewed, and the new result stating structural uncontrollability, of the sensitivity, system for normal systems having the number of independent parameters not smaller than twice the number of control variables is proved.     

Further remarks on the controllability of linear constant delay-differential systems

Function space null controllability is considered for certain delay-differential systems. The implications of the input-decoupling factors and input-decoupling zeros of the corresponding system matrices are considered.     

Further results on controllability of recurrent neural networks

This paper studies controllability properties of recurrent neural networks. The new contributions are: (1) an extension of a previous result to a slightly different model, (2) a formulation and proof of a necessary and sufficient condition, and (3) an analysis of a low-dimensional case for which the hypotheses made in previous work do not apply.     

Further results on controllability properties of discrete-time nonlinear systems

Controllability questions for discrete-time nonlinear systems are addressed in this paper. In particular, we continue the search for conditions under which the group-like notion of transitivity implies the stronger and semigroup-like property of forward accessibility. We show that this implication holds, pointwise, for states which have a weak Poisson stability property, and globally, if there exists a global attractor for the system.This research was supported in part by US Air Force Grant AFOSR-91-0346, and also by an INDAM (Istituto Nazionale di Alta Matematica Francesco Severi, Italy) fellowship.     

A schmidt type process for the solution of Ax=b

An orthogonalization type algorithm is presented for the triangularization of the coefficient matrix of a system of linear algebraic equations. A backward error analysis is performed on the algorithm. Some numerical examples are presented. The algorithm is extended in order to perform the complete forward reduction.     

Further results on linear nonquadratic optimal control

Continues an investigation by the authors of minimizing the transient response of a linear system as measured by nonquadratic penalty functions, in particular, penalty functions which have linear growth. First, this note shows that the optimal state feedback which minimizes the transient response in the case of no exogenous inputs also minimizes the induced l¹ norm in case exogenous inputs are present. Second, it considers the case of constrained systems and derives bounds which establish the stability and performance of receding horizon control laws. Finally, this note illustrates the results for scheduling of reliable manufacturing systems     

Iterative solvers of Ax = b derived from ode's numerical integration methods

Although iterative methods for solving linear systems has been the subject of study for a long time, the acceleration of such methods is still object of interest, research focusing in improvements of already known methods as well as on new, faster ones. In this sense we can cite among several other authors, for example, the works of Martins [8], Hadjidimos [9] and Evans [7]. The purpose of this paper is twofold. First we show that the numerical integration methods for Ordinary Differential Equations, obtained by Taylor expansions, result in a B-extrapolation method [3] for iteratively solving linear algebraic systems. Second, we compare the best rates of convergence of the algorithms developed here, with the best rate of convergence of the Jacobi Over-Relaxation method, (JOR), proving that depending on the choice of the step of integration and the behavior of the spectrum of the matrix A of the original system Ax = b the third order methods derived from the Taylor expansions can be better than the JOR. The procedure used here with the splitting A – I – J can also be easely applied to other splittings, resulting in a comparison of the convergence of the present method with the SOR or iterations methods or any other linear iterative methods of degree one.     

Further results on the delay-independent asymptotic stability of linear systems

New sufficient conditions for delay-independent asymptotic stability and decaying rale for linear systems are presented. The superiority of these results is demonstrated by comparing them to those given in the literature.     

SYMMLQ-like procedure for Ax = b where A is a special normal matrix

Abstract We propose a method of Lanczos type for solving a linear system with a normal matrix whose spectrum is contained in a second-degree curve. This is a broader class of matrices than that of the (l,m)-normal matrices introduced in a recent paper by Barth and Manteuffel. Our approach is similar to that of Huhtanen in the sense that both use the condensed form of normal matrices discovered by Elsner and Ikramov. However, there are a number of differences, among which are: (i) our method is modeled after the SYMMLQ algorithm of Paige and Saunders; (ii) it uses only one matrix-vector product per step; (iii) we provide effective means for monitoring the size of the residual during the process. Numerical experiments are presented. Keywords: generalized Krylov sequence, Rayleigh-Ritz projection, SYMMLQ algorithm, GMRES algorithm, normal matrix     

Null controllability of a linear KdV equation on an interval with special boundary conditions

In this paper, we deal with the null controllability of a linear Korteweg-de Vries equation with special boundary conditions. We first study the Cauchy problem and prove the existence and uniqueness of solutions in suitable spaces, and then prove the null controllability of this system by establishing an observability inequality which is proved with the help of a Carleman estimate.     

Further on the controllability of networked MIMO LTI systems

Further on the controllability of networked multiple‐input–multiple‐output systems, an efficient, necessary, and sufficient condition is derived, where the network topology is directed and weighted and the nodes are higher‐dimensional linear time‐invariant systems. The new condition is easier to verify, which explicitly shows the effects of the network topology, node‐system dynamics, external control inputs, and inner interactions on the controllability of the whole networked system. For networked multiple‐input–multiple‐output systems in several specific topologies, the corresponding conditions are expressed more precisely. The effectiveness of the conditions is demonstrated through several examples.     

More on the controllability of linear time-invariant systems

This study shows that a controllable system [xdot] = Ax + Bu, where x is an n-vector, can be driven from an arbitrary initial condition x(0) = x₀ to an arbitrary final condition x(t_f = x_f by a polynomial control function of degree M = 2r + 1, where r = n ? rank (B), through a polynomial trajectory of degree M. A simple algorithm for finding u by solving a set of linear equations, the solution of which yields the polynomial coefficients, is given.     

Complete controllability and controllability for linear autonomous systems of neutral type

We solve the complete controllability problem for linear autonomous systems of neutral type with many commensurable delays in the case when a system solution is required to be an absolutely continuous functions. We propose a control method for the said objects if they do not have the complete controllability property.     

Further results on structural assignment of linear systems via sensor selection

The problem of assigning structural properties of a linear system through sensor selection is, for a given pair (A,B), to find an output pair (C,D) such that the resulting system (A,B,C,D) has the pre-specified structural properties, such as the finite and infinite zero structures and the invertibility properties. In this paper, by introducing the notion of infinite zero assignable sets for the pair (A,B), we establish necessary and sufficient conditions for the assignability of a given set of infinite zeros and a set of structural properties which includes the left invertibility property. In establishing these conditions, we develop a numerical algorithm for the construction of the required (C,D).