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.     

Contracted product of hypermatrices via STP of matrices

An equivalent definition of hypermatrices is introduced. The matrix expression of hypermatrices is proposed. Using permutation matrices, the conversion between different matrix expressions is revealed. The various kinds of contracted products of hypermatrices are realized by semi-tensor products (STP) of matrices via matrix expressions of hypermatrices.     

Exact speedup factors and sub-optimality for non-preemptive scheduling

Fixed priority scheduling is used in many real-time systems; however, both preemptive and non-preemptive variants (FP-P and FP-NP) are known to be sub-optimal when compared to an optimal uniprocessor scheduling algorithm such as preemptive earliest deadline first (EDF-P). In this paper, we investigate the sub-optimality of fixed priority non-preemptive scheduling. Specifically, we derive the exact processor speed-up factor required to guarantee the feasibility under FP-NP (i.e. schedulability assuming an optimal priority assignment) of any task set that is feasible under EDF-P. As a consequence of this work, we also derive a lower bound on the sub-optimality of non-preemptive EDF (EDF-NP). As this lower bound matches a recently published upper bound for the same quantity, it closes the exact sub-optimality for EDF-NP. It is known that neither preemptive, nor non-preemptive fixed priority scheduling dominates the other, in other words, there are task sets that are feasible on a processor of unit speed under FP-P that are not feasible under FP-NP and vice-versa. Hence comparing these two algorithms, there are non-trivial speedup factors in both directions. We derive the exact speed-up factor required to guarantee the FP-NP feasibility of any FP-P feasible task set. Further, we derive the exact speed-up factor required to guarantee FP-P feasibility of any constrained-deadline FP-NP feasible task set.     

Fixed priority pre-emptive scheduling: An historical perspective

From its roots in job-shop scheduling, research into fixed priority pre-emptive scheduling theory has progressed from the artificial constraints and simplistic assumptions used in early work to a sufficient level of maturity that it is being increasingly used in the implementation of real-time systems. It is therefore appropriate that within this special issue we provide an historical perspective on the development of fixed priority pre-emptive scheduling.     

A review of priority assignment in real-time systems

It is over 40 years since the first seminal work on priority assignment for real-time systems using fixed priority scheduling. Since then, huge progress has been made in the field of real-time scheduling with more complex models and schedulability analysis techniques developed to better represent and analyse real systems. This tutorial style review provides an in-depth assessment of priority assignment techniques for hard real-time systems scheduled using fixed priorities. It examines the role and importance of priority in fixed priority scheduling in all of its guises, including: pre-emptive and non-pre-emptive scheduling; covering single- and multi-processor systems, and networks. A categorisation of optimal priority assignment techniques is given, along with the conditions on their applicability. We examine the extension of these techniques via sensitivity analysis to form robust priority assignment policies that can be used even when there is only partial information available about the system. The review covers priority assignment in a wide variety of settings including: mixed-criticality systems, systems with deferred pre-emption, and probabilistic real-time systems with worst-case execution times described by random variables. It concludes with a discussion of open problems in the area of priority assignment.     

分布式嵌入式系统实时调度的建模

针对RBTPN模型在建模分布式嵌入式系统实时调度时的不足,提出了一种新的扩展时间Petri网模型。该模型通过在需要处理器资源的变迁上引入变迁速率因子,得到具有相同优先级变迁的运行速率函数,从而在分布式嵌入式系统的调度建模中,在单个处理器上结合了固定优先级可抢先调度和轮转调度。随后给出了该模型可达图的构造方法,以便可以得到调度序列的各种性质。     

The Non-Optimality of the Monotonic Priority Assignments for Hard Real-Time Offset Free Systems

In this paper, we study the problem of scheduling hard real-time periodic tasks with static priority pre-emptive algorithms. We consider tasks which are characterized by a period, a hard deadline, a computation time and an offset (the time of the first request), where the offsets may be chosen by the scheduling algorithm, hence the denomination offset free systems.We study the rate monotonic and the deadline monotonic priority assignments for this kind of system and we compare the offset free systems and the asynchronous systems in terms of priority assignment. Hence, we show that the rate and the deadline monotonic priority assignments are not optimal for offset free systems.     

Energy aware fixed priority scheduling in mixed-criticality systems

Most of studies about energy management for MC systems are based on dynamic priority scheme. The disadvantages of dynamic priority scheme are high system overhead and poor predictability. Unlike previous studies, we focus on the problem of scheduling mixed-criticality (MC) periodic tasks with minimizing energy consumption in MC systems based on fixed priority scheme. Firstly, we explain a criticality rate monotonic scheduling (CRMS) and propose the sufficient schedulability condition of CRMS. Secondly, we compute the energy minimization uniform scaled speed and present an optimal static solution algorithm based on CRMS. The extra workload of the high criticality level (HI) task executes with the maximum processor speed in the high criticality mode (HI-mode). But this algorithm does not exploit the slack time generated from the HI task in the low criticality mode (LO-mode). For energy efficiency, we propose a dynamic fixed priority energy minimization algorithm which exploits the slack time generated from the HI task in LO-mode to save energy. In addition, it combines a dynamic voltage and frequency scaling technique and a dynamic power management technique to reduce energy consumption. Finally, the experiments are applied to evaluate the performance of the proposed algorithm and the experimental results show that the proposed algorithm can save up 23.89% energy compared with other existing algorithms.     

周期多帧任务的固定优先级调度算法的调度分析

实时操作系统的核心问题－－实时任务的调度是实时系统研究的重点之一。主要讨论了周期多帧任务的固定优先级调度算法的调度情况,证明了对于周期多帧任务DM算法不是最优的,同时也证明了对于累积单调周期多帧任务的DM算法是最优的。     

FPSL, FPCL and FPZL schedulability analysis

This paper presents the Fixed Priority until Static Laxity (FPSL), Fixed Priority until Critical Laxity (FPCL) and Fixed Priority until Zero Laxity (FPZL) scheduling algorithms for multiprocessor real-time systems. FPZL is similar to global fixed priority pre-emptive scheduling; however, whenever a task reaches a state of zero laxity it is given the highest priority. FPSL and FPCL are variants of FPZL that introduce no additional scheduling points beyond those present with fixed priority scheduling. FPSL, FPCL and FPZL are minimally dynamic algorithms, in that the priority of a job can change at most once during its execution, bounding the number of pre-emptions. Polynomial time and pseudo-polynomial time sufficient schedulability tests are derived for these algorithms. The tests are then improved by computing upper bounds on the amount of execution that each task can perform at the highest priority. An empirical evaluation shows that FPSL, FPCL, and FPZL are highly effective, with a significantly larger number of tasksets deemed schedulable by the tests derived in this paper, than by state-of-the-art schedulability tests for EDZL scheduling.     

模糊数据流实时任务调度算法

针对数据流系统中实时查询任务的特点,提出了基于模糊综合评判的动态优先级调度算法。用语言模糊集描述任务的不确定性因素和不同的优先等级,利用最大隶属度原理确定任务的优先等级。算法充分考虑了任务的持续周期性、任务之间存在依赖关系与共享滑动窗口的特点对任务优先级的影响。从累积实现价值率、差分截止期保证率和CPU切换频率3个方面测试了算法的性能,实验表明所提出算法相对于HVF算法、LSF算法、模糊动态抢占调度算法都有很大的改进。     

端到端实时CORBA系统调度模型及其可调度性研究

实时CORBA系统中的基本问题是如何合理分配有限的计算资源和通信资源以保证各个实时任务的时间需求。该文以固定优先级方式调度的、周期性任务的硬实时系统为研究对象，提出了端到端实时CORBA系统调度模型，该模型综合考虑了客户端系统的处理、服务对象处理、网络传输等几大主要因素，而且可以描述服务对象间的嵌套调用关系，因而能全面描述实时CORBA系统中客户调用过程。在此基础上，该文基于非连续工作型同步协议，应用时间需求分析方法，研究并提出了该模型的可调度性分析算法。