In this paper we investigate the minimum amount of input power required to estimate a given linear system with a prescribed degree of accuracy, as a function of the model complexity. This quantity is defined to be the ‘cost of complexity’. The degree of accuracy considered is the maximum variance of the discrete-time transfer function estimator over a frequency range [−ωB, ωB]. It is commonly b...

A realization problem for positive, continuous-time linear systems with reduced numbers of delays in state and in control is formulated and solved. Sufficient conditions for the existence of positive realizations with reduced numbers of delays of a given proper transfer function are established. A procedure for the computation of positive realizations with reduced numbers of delays is presented...

In this contribution aspects of inter sample input signal behavior are examined The starting point is that parametric identi cation always is performed on basis of discrete time data This is valid for identi cation of discrete time models as well as continuous time models The usual assumptions on the input signal are i it is band limited ii it is piecewise constant or iii it is piecewise linear...

In this paper we derive formulas for constructing the analytic center of the linear matrix inequality deening a positive (para-hermitian) transfer function. The Riccati equations that are usually associated with such positive transfer functions, are related to boundary points of the convex set. In this paper we show that the analytic center is also described by a closely related equation, and w...

The paper consists of two parts. In the first part, new canonical forms are defined for singular 1D linear systems and a procedure to determine nonsingular matrices transforming matrices of singular systems to their canonical forms is derived. In the second part new canonical forms of matrices of the singular 2D Roesser model are defined and a procedure for determining realisations in canonical...

We extend the approximate transfer function calculus of “undersnreadll linear time-varvine fLTV1 svstems introduced by W. Kozek. Our extensiog is‘ based o”n a new, generalized definition of underspread LTV svstems that does not assume finite support of the systems”’ spreading function. We establish explicit bounds on various error quantities associated with the transfer function approximation. ...

The paper establishes the design procedure for the state feedback control of linear discrete-time systems, considerable as an interposed design criterium in the form of linear matrix inequalities. The goal is to design the feedback control which guarantees bounded H2 performance index for the system transfer function matrix and H∞ norm attenuation for the disturbance transfer function matrix, b...

In this paper, we study the existence of linear quadratic Gaussian (LQG)–balanced realizations for discrete-time infinite-dimensional systems. LQG-balanced realizations are those for which the smallest nonnegative self-adjoint solutions of the control and filter Riccati equations are equal. We show that the control (filter) Riccati equation has a nonnegative self-adjoint solution if and only if...

Fault Detection and Isolation (FDI) problems are here considered for linear systems with faults and disturbances. We design a set of observer-based residuals, in such a way that the transfer from the disturbances to the residuals is zero and the transfer from the faults to the residuals allows fault isolation. We are interested in obtaining a transfer function from faults to residuals with eith...

1. What is Model Reduction? 1.1. Single Component Model Reduction 1.2. Multi-Component Model Reduction 1.3. The Quality of the Reduced Order Model 1.4. Characterization of the Single-Component Model Reduction Error 2. Linear System Properties 2.1. Input-Output Transfer Function 2.2 Controllability and Observability 2.3. Frequency Moments and Markov Parameters 2.4. Output Correlation and Power M...