Invariant zeros of SISO infinite-dimensional systems

The zeros of a finite-dimensional system can be characterised in terms of the eigenvalues of an operator on the largest closed feedback-invariant subspace. This characterisation is also valid for infinite-dimensional systems, provided that a largest closed feedback-invariant subspace exists. We generalise this characterisation of the zeros to the case when the largest closed feedback-invariant subspace does not exist. We give an example which shows that the choice of domain of the operator on this invariant subspace is crucial to this characterisation.     

Relationship between poles and zeros of input–output and chain-scattering systems

A system is frequently represented by transfer functions in an input–output characterization. However, such a system (under mild assumptions) can also be represented by transfer functions in a port characterization, frequently referred to as a chain-scattering representation. Due to its cascade properties, the chain-scattering representation is used throughout many fields of engineering. This paper studies the relationship between poles and zeros of input–output and chain-scattering representations of the same system.     

Autotune identification for systems with right-half-plane poles and zeros

Autotuning based on relay feedback tests have received a great deal of attention recently. The relay feedback tests fail to generate sustained oscillation in some cases. For systems with RHP poles and/or zeros, incorrect autotune identification procedure may give erroneous information and unstable limit cycle. Frequency domain analyses provide a criteria for prediction of the existence of stable limit cycle. Furthermore, a procedure is given to ensure the success of a relay feedback test. The analyses and procedure are illustrated through open loop stable and unstable systems. Results show that, except for some rare occasion, successful relay feedback experiments can be obtained following the proposed procedure.     

Achievable performance of multivariable systems with unstable zeros and poles

This paper examines the fundamental limitations imposed by unstable (right half plane; RHP) zeros and poles in multivariable feedback systems. We generalize previously known controller-independent lower bounds on the H     

Model reduction of systems with zeros interlacing the poles

The problem of reducing a system with zeros interlacing the poles (ZIP) on the real axis is considered. It is proved that many model reduction methods, such as the balanced truncation, balanced residualization, suboptimal and optimal Hankel approximations, inherit the ZIP property. Properties of the Hankel singular values of ZIP systems are also listed.     

Right half plane poles and zeros and design tradeoffs in feedback systems

This paper expresses limitations imposed by right half plane poles and zeros of the open-loop system directly in terms of the sensitivity and complementary sensitivity functions of the closed-loop system. The limitations are determined by integral relationships which must be satisfied by these functions. The integral relationships are interpreted in the context of feedback design.     

Variance-error quantification for identified poles and zeros

This paper deals with quantification of noise induced errors in identified discrete-time models of causal linear time-invariant systems, where the model error is described by the asymptotic (in data length) variance of the estimated poles and zeros. The main conclusion is that there is a fundamental difference in the accuracy of the estimates depending on whether the zeros and poles lie inside or outside the unit circle. As the model order goes to infinity, the asymptotic variance approaches a finite limit for estimates of zeros and poles having magnitude larger than one, but for zeros and poles strictly inside the unit circle the asymptotic variance grows exponentially with the model order. We analyze how the variance of poles and zeros is affected by model order, model structure and input excitation. We treat general black-box model structures including ARMAX and Box–Jenkins models.     

Stability tests and stabilization for piecewise linear systems based on poles and zeros of subsystems

This paper provides several stability tests for piecewise linear systems and proposes a method of stabilization for bimodal systems. In particular, we derive an explicit and exact stability test for planar systems, which is given in terms of coefficients of transfer functions of subsystems. Restricting attention to the bimodal and planar case, we show simple stability tests. In addition, we drive a necessary stability condition and a sufficient stability condition for higher-order and bimodal systems. They are given in terms of the eigenvalue loci and the observability of subsystems. All the stability tests provided in this paper are computationally tractable, and our results are applied to the stabilizability problem. We confirm the exactness and effectiveness of our approach by illustrative examples.     

On undershoot in SISO systems

We show that the step response of an asymptotically stable strictly proper nonminimum phase continuous time system with m₁ real open right half plane zeros, no conjugate complex zeros and poles, and with real open left half plane zeros and poles satisfying a given “bracketing” condition, exhibits undershoot exactly int m₁+½ times. Both qualitative and quantitative arguments are also introduced to highlight the main issues under discussion. Simple examples are given to illustrate and complement the main result of this paper     

The output stabilization of SISO bilinear systems

A quite general approach to the problem of stabilizing a SISO (single-input single-output) bilinear system by output feedback is presented. Following a Lyapunov-like method, a family of admissible controls is defined and an easy way for deriving its general features is proposed. Previous results can be obtained as special cases of this approach. Numerical examples are included to show the feasibility of this algorithm in determining simple control laws     

The finite zeros of diminished systems

The assignment and preservation of the finite zeros of multivariable systems is considered when selected inputs and outputs are combined to form now input-output transferences. Conditions are given under which all of the finite zeros of the newly formed ‘ diminished system ’ can be assigned arbitrarily. The results have some features in common with the more widely known conditions under which all of the poles of a system can be relocated using constant output feedback. One consequence of the results is that further insight can be obtained into a well known zero assignment algorithm due to Kouvaritakis and MacFarlane (1976 a, b). The results have relevance to the problem of ‘ squaring down ’ a non-square system.     

Robustness of a design method based on assignment of poles and zeros

The sensitivity of a pole-zero placement design with respect to variations in the process model is discussed. Inequalities which guarantee stability and precision in the assigned poles are given.     

Identification and adaptive control of SISO singular systems

A general adaptive control scheme is presented for an unknown time invariant singular system of the form Ex(t + 1) = Ax(t) + Bu(t); y(t) = Cx(t). Owing to the non-causality of this kind of system, the identification of unknown parameters is re-considered and a new residual signal is constructed and used in the recursive calculations. A general design procedure is obtained that uses the identified parameters and includes two steps: (i) preliminary output feedback gain design in order to make the original system causal; (ii) adaptive control design for the causal system. It has been shown that any adaptive control algorithm can be combined with this scheme to obtain a globally stable closed-loop system. The design procedure is shown to perform well on a simulation of a third-order singular system     

The relationship between environmental management systems and organizational innovations

This study provides empirical evidence of the nature of the relationship between environmental management systems and organizational innovations. Using a sample of Spanish manufacturing firms, the study reports on the implementation of the International Organization for Standardization (ISO) 14000 environmental quality standards and the relationship of such implementation with organizational innovations in the firm. The study presents several implications of interest for practitioners, academics, and policy makers. © 2012 Wiley Periodicals, Inc.     

The design of multivariable systems having zero sensitive poles

A design technique that assigns the maximal number of poles of a linear multivariable system and makes them insensitive to uncertainty in the parameters of the system dynamical matrix is introduced. Its immediate application is in multivariable dominant poles design.     

The relationship of controllability between classical and fuzzy discrete-event systems

We have known that the controllability of classical discrete-event systems has already been extended into fuzzy discrete-event systems. In this paper, firstly, we recall some related definitions and results of the controllability for classical and fuzzy discrete-event systems, respectively. Secondly, we are concerned with the relationship of the controllability between classical and fuzzy discrete-event systems. In particular, we show that there is an equivalence of the controllability between the two systems to some extent, some special proofs are also presented. Finally, we use this equivalence to extend some general controllability properties of classical discrete-event systems into fuzzy ones.     

On nonachievable frequency domain specifications in SISO feedbackcontrol systems

It is shown how bounds on the sensitivity function and the complementary sensitivity function which are not simultaneously achievable by any stabilizing controller can be computed by means of the H_∞ approach. This allows evaluation of a given synthesis in terms of its distance from nonachievable specifications and provides information about design tradeoffs