Some applications of matrices to location of zeros of polynomials†

In previous papers classical theorems on location of zeros of a polynomial with respect to the left half plane Γ₁ or the unit circle Γ₂ have been reformulated more simply in terms of appropriate companion matrices. It is shown how this work can be extended to the problem of zero location with respect to more general regions Γ of the complex plane. The first approach is to apply the bilinear transformation to the given polynomial, so that for example Γ₁ can be mapped into Γ₂ and a matrix representation of this is derived. An alternative method is discussed which relies on transformation of Γ into Γ₂. Some examples illustrate how any theorem involving Hurwitz-typc minors can be expressed in companion matrix terms, with a consequent halving of the orders of the determinants involved.     

The Implementation of Graphic Display of FAS

The principle of the fire alarm system and the implementation techniques of its computer graphic display are presented. With the help of the designing thoughts and technology of OOP, a Fire Alarm System (FAS) has been developed by using visual C++ language. The system has been put into use in many important buildings and has played an important role in monitoring and controlling the fire.     

Measurement of the Kernels of a Non-linear System of Finite Order†

A method of measuring the Volterra kernels of a finite-order non-linear system is presented. The kernels are obtained individually as a multi-dimensional impulse response. The multi-dimensional kernel transforms also can be obtained by the method described. As an extension, a technique of obtaining the Volterra kernels from a multi-dimensional step response is presented. This technique is useful for non-linear systems which can be considered to be of a given finite order for only a limited range of input amplitudes.     

Evaluation of Fourier transform of impulse response of linear time invariant systems†

Evaluation of the Fourior transform of the system impulse response is an important aspect of the design of control systems. A method suggested hero requires only one cycle of sine or cosine wave to be applied as an input to the system. It is proved that the sum of the sampled values of the output response, at the sampling interval equal to the period of the input wave, directly yields the sign and cosine transforms respectively. The procedure is generalized to any number of complete cycles of input wave, as well as to n/2 cycles whore n is any odd positive integer.     

Optimization of linear systems of constrained configuration†

For the sake of simplicity it is often desirable to restrict the number of feedbacks in a controller. In this case the optimal feedbacks depend on the disturbance to which the system is subjected. Using a quadratic error integral as a measure of the response, three criteria of optimization are considered :

1. The response to a given initial disturbance.

2. The worst response to an initial disturbance of given magnitude.

3. The worst comparison with the unconstrained optimal system.

It is shown that for each of these criteria the gradient with respect to the feedbacks can be calculated by a uniform method. The solution may then be found either directly or by a descent procedure. The method is illustrated by an example.     

Stabilization of a class of switched nonlinear systems

The stabilization of a class of switched nonlinear systems is investigated in the paper. The systems concerned are of （generalized） switched Byrnes-Isidori canonical form, which has all switched models in （generalized） Byrnes- Isidori canonical form. First, a stability result of switched systems is obtained. Then it is used to solve the stabilization problem of the switched nonlinear control systems. In addition, necessary and sufficient conditions are obtained for a switched affine nonlinear system to be feedback equivalent to （generalized） switched Byrnes-Isidori canonical systems are presented. Finally, as an application the stability of switched lorenz systems is investigated.     

Fault-tree Models of Accident Scenarios of RoPax Vessels

Ro-Ro vessels for cargo and passengers (RoPax) are a relatively new concept that has proven to be popular in the Mediterranean region and is becoming more widespread in Northern Europe. Due to its design characteristics and amount of passengers, although less than a regular passenger liner, accidents with RoPax vessels have far reaching consequences both for economical and for human life. The objective of this paper is to identify hazards related to casualties of RoPax vessels. The terminal casualty events chosen are related to accident and incident statistics for this type of vessel. This paper focuses on the identification of the basic events that can lead to an accident and the performance requirements. The hazard identification is carried out as the first step of a Formal Safety Assessment (FSA) and the modelling of the relation between the relevant events is made using Fault Tree Analysis (FTA). The conclusions of this study are recommendations to the later steps of FSA rather than for decision making (Step 5 of FSA). These recommendations will be focused on the possible design shortcomings identified during the analysis by fault trees throughout cut sets. Also the role that human factors have is analysed through a sensitivity analysis where it is shown that their influence is higher for groundings and collisions where an increase of the initial probability leads to the change of almost 90% of the accident occurrence.     

On the Equivalence of Some Models of Computation

In[1],a definition of computation was given.In[3],we have clarified the necessity of thedefinition.Here we prove the equivalence between the definition and some models ofcomputation.Hence the sufficiency of the definition is clear abundantly.     

A Form-Correcting System of Chinese Characters Using a Model of Correcting Procedures of Calligraphists

A support system for form-correction of Chinese Characters is developed based upon a generation model SAM,and its feasibility is evaluated.SAM is excellent as a model for generating Chinese characters,but it is difficult to determine appropriate parameters because the use of calligraphic knowledge is needed.by noticing that calligraphic knowledge of calligraphists is included in their corrective actions, we adopt a strategy to acquire calligraphic knowledge by monitoring,recording and analyzing corrective actions of calligraphists,and try to realize an environment under which calligraphists can easily make corrections to character forms and which can record corrective actions of calligraphists without interfering with them.In this paper,we first construct a model of correcting procedures of calligraphists,which is composed of typical correcting procedures that are acquired by extensively observing their corrective actions and interviewing them,and develop a form-correcting system for brush-written Chinese characters by using the model.Secondly,through actual correcting experiments,we demonstrate that parameters within SAM can be easily corrected at the level of character patterns by our system,and show that it is effective and easy for calligraphists to be used by evaluating effectiveness of the correcting model,sufficiency of its functions and execution speed.     

Solution of the Problem of H∞-control in the Presence of Regular Nonlinearities

For the problem with H-criterion and uncertain nonlinear block with a regular part of the perturbation vector, equations of a class of controllers were obtained. These controllers can exert a sufficiently small influence of the regular component on the given output process.     

Reliable observer-based H∞ control of uncertain state-delayed systems

This paper is concerned with the reliable H_∞ control design problem for linear state-delayed system using observed-based output feedback. It proposes a reliable control design scheme for the case of possibly a simultaneous presence of actuator failures and sensor failures. Modified algebraic Riccati inequalities are developed to solve the problem addressed. Based on this approach, observer-based feedback control laws are designed that guarantee closed-loop asymptotic stability and reduction of the effect of an augmented disturbance input on the controlled output of a prescribed level, not only when the system is operating properly, but also under actuator and sensor failures. A numerical example is presented to demonstrate the applicability and effectiveness of the proposed approach.     

Robust Reliable H∞ Control for Discrete‐Time Systems with Actuator Delays

This article focuses on the robust state feedback reliable H_∞ control problem for discrete‐time systems. Discrete‐time systems with time‐varying delayed control input are formulated. Based on the Lyapunov–Krasovskii method and linear matrix inequality (LMI) approach, delay‐dependent sufficient conditions are developed for synthesizing the state feedback controller for an uncertain discrete‐time system. The parameter uncertainty is assumed to be norm bounded. A design scheme for the state feedback reliable H_∞ controller is proposed in terms of LMIs, which can guarantee the global asymptotic stability and the minimum disturbance attenuation level. Finally, numerical examples are provided to illustrate the effectiveness and reduced conservatism of the proposed methods.     

LMI optimization approach to robust H∞ observer design and static output feedback stabilization for discrete‐time nonlinear uncertain systems

A new approach for the design of robust H_∞ observers for a class of Lipschitz nonlinear systems with time‐varying uncertainties is proposed based on linear matrix inequalities (LMIs). The admissible Lipschitz constant of the system and the disturbance attenuation level are maximized simultaneously through convex multiobjective optimization. The resulting H_∞ observer guarantees asymptotic stability of the estimation error dynamics and is robust against nonlinear additive uncertainty and time‐varying parametric uncertainties. Explicit norm‐wise and element‐wise bounds on the tolerable nonlinear uncertainty are derived. Also, a new method for the robust output feedback stabilization with H_∞ performance for a class of uncertain nonlinear systems is proposed. Our solution is based on a noniterative LMI optimization and is less restrictive than the existing solutions. The bounds on the nonlinear uncertainty and multiobjective optimization obtained for the observer are also applicable to the proposed static output feedback stabilizing controller. Copyright © 2008 John Wiley & Sons, Ltd.     

Resilient H∞ Control Design for Discrete‐Time Uncertain Linear Systems: An Auxiliary System Transformation Approach

This paper studies the resilient (non‐fragile) H∞ output‐feedback control design for discrete‐time uncertain linear systems with controller uncertainty. The design considers parametric norm‐bounded uncertainty in all state‐space matrices of the system, output and controller equations. The paper shows that the resilient H∞ output‐feedback control problem is equivalent to a scaled H∞ output‐feedback control problem of an auxiliary system without any system or controller uncertainty. Using the existing optimal H∞ design to solve the auxiliary system, the design guarantees that the resultant closed‐loop systems are quadratically stable with disturbance attenuation γ for all admissible system and controller uncertainties. A numerical example is given to illustrate the design method and its benefits.     

H∞control of interconnected nonlinear sampled-data systems with parametric uncertainty

This paper studies the problem of robust control design for a class of interconnected uncertain systems under sampled measurements. The class of system under consideration is described by a state space model containing unknown cone bounded nonlinear interaction and time-varying norm-bounded parameter uncertainties in both state and output equations. Our attention is focused on the design of linear dynamic output feedback controllers using sampled measurements. We address the problem of robust H_∞ control in which both robust stability and a prescribed H_∞ performance are required to be achieved irrespective of the uncertainties and nonlinearities. The H_∞ performance measure involves both continuous-time and discrete-time signals. It has been shown that the above problems can be recast into H_∞ syntheses for related N decoupled linear sampled-data systems without parameter uncertainties and unknown nonlinearities, which can be solved in terms of Riccati differential equations with finite discrete jumps. A numerical example is given to show the potential of the proposed technique.     

A new approach to robust reliable H∞ control for uncertain nonlinear systems

This paper focuses on the optimal robust reliable H_∞ control for a class of uncertain nonlinear systems with actuator faults. A new method of annihilating uncertain matrix is proposed. Based on this approach, a new method of disposing of the phenomenon of uncertain matrices multiplication is provided. In accordance with the method, the optimal robust reliable H_∞ control problem for uncertain nonlinear systems is settled by employing state feedback, in terms of linear matrix inequality (LMI). Finally, two illustrative examples are given to show the feasibility and validity of the proposed method.     

Robust H∞ Controller Design for Uncertain Neutral Systems via Dynamic Observer Based Output Feedback

In this paper, the dynamic observer-based controller design for a class of neutral systems with H∞ control is considered. An observer-based output feedback is derived for systems with polytopic parameter uncertainties. This controller assures delay-dependent stabilization and H∞ norm bound attenuation from the disturbance input to the controlled output. Numerical examples are provided for illustration and comparison of the proposed conditions.     

H∞ output feedback control for fuzzy systems with immeasurable premise variables: Discrete-time case

This paper discusses H_∞ output feedback control of discrete-time Takagi–Sugeno fuzzy systems with immeasurable premise variables. When we consider the output feedback control of Takagi–Sugeno fuzzy systems, the selection of premise variables plays an important role. If the premise variable is the state of the system, then a fuzzy system describes a wide class of nonlinear systems. However, the state is not measurable in the output feedback control problem. In this case, a control design of the underlying nonlinear system based on parallel distributed compensation is infeasible because a controller depends on the immeasurable state variable. In this paper, we introduce a new method to treat fuzzy systems with immeasurable premise variables and consider a design method of H_∞ output feedback control problem. We formulate this fuzzy control problem as a robust H_∞ control of an uncertain system. Numerical examples are given to illustrate our methods.     

Reliable H ∞ control of multiple time scales singularly perturbed systems with sensor failure

This paper studies the reliable H _∞ control for linear time-invariant multiparameter singularly perturbed systems against sensor failures. By time-scale decomposition, the full-order system is decomposed into slow and fast subsystems. After designing a reliable H _∞ controller for the global system, three reduced reliable H _∞ sub-controllers based on the slow and fast problems are obtained through the manipulation of the algebraic Riccati equations. The resulting control systems are reliable in that they provide guaranteed asymptotic stability and H _∞ performance when all control components are operational as well as when sensor failures occur.     

Quadratic stabilizability and H∞ control of linear discrete‐time stochastic uncertain systems

This paper considers quadratic stabilizability and H_∞ feedback control for stochastic discrete‐time uncertain systems with state‐ and control‐dependent noise. Specifically, the uncertain parameters considered are norm‐bounded and external disturbance is an l²‐square summable stochastic process. Firstly, both quadratic stability and quadratic stabilization criteria are presented in the form of linear matrix inequalities (LMIs). Then we design the robust H_∞ state and output feedback H_∞ controllers such that the system with admissible uncertainties is not only quadratically internally stable but also robust H_∞ controllable. Sufficient conditions for the existence of the desired robust H_∞ controllers are obtained via LMIs. Finally, some examples are supplied to illustrate the effectiveness of our results.