Verifying fragility in digital systems with uncertainties using DSVerifier v2.0

The Lyapunov function method is used to study the robust absolute stability of general interval Lurie control systems, and algebraic sufficient conditions are obtained for the general interval Lurie type control systems. A relationship between the stability of the symmetric interval matrix and robust absolute stability of general interval Lurie type control systems is established.

The use of avionics networks for flight control system has reduced aircraft weight, system installation, integration and maintenance costs as well as introduced time delays and structured uncertainties. This paper studies the robust stability and stabilisation problem of uncertain networked flight control system with random time delays. Some new sufficient criteria with simple mathematical forms for robust stability and stabilisation of networked flight control system are derived by a free weighting matrix approach. A memoryless state feedback robust controller and the maximum bound of time delay are obtained based on the solution of linear matrix inequalities (LMIs) which are established by the Lyapunov-Krasovskii stability theory. Numerical examples are given to illustrate the effectiveness of design procedure.

This article presents a design method for translating a finite impulse response (FIR) floating-point multiplierless filter design. Conventional wisdom dictates that finite word-length (i.e., quantization) effects can be minimized by dividing a filter into smaller, cascaded sections. In this design method, it is shown how to quantize the cascaded sections so that the finite word-length effects in one section are guaranteed to compensate for the finite word-length effects in the other section. This simple method called, compensating zeros, ensures that: (1) the quantized filter's frequency response closely matches the unquantized filter's frequency response (in both magnitude and phase); and (2) the required hardware remains small and fast.

The effects of finite word length on arithmetic codes are studied. Four causes of performance degradation are identified. Emphasis is placed on the major source of the degradation, i.e., finite word-length registers used to compute the arithmetic codes. Theoretical analysis and computer simulation of this effect are presented. It is found that this degradation is proportional to the size of the alphabet and is reduced by half for each bit of increased word-length. >

Covariance matrix adaptation evolution strategy based design of fixed structure robust H∞ loop shaping controller

The robust stability criterion for sampled-data control systems with a sector nonlinearity was presented in our previous papers (1996, 1998). Although it is applicable only to the sampled-data control system of a certain class, a usual discrete-time control system belongs to this type of class. The criterion contains the robust stability condition in regard to the nonlinear allowable band (sector) for continuous-time systems and the linear allowable gain band (interval set) for discrete-time systems. The paper focuses primarily on the concept of robust stability in order to analyze a nonlinear element by the linear gain band, in other words, the validity of Aizerman's conjecture extended into discrete-time systems.

In this paper, we consider generalized delay-dependent stability conditions of Takagi-Sugeno fuzzy systems with discrete and distributed time-delays. For fuzzy systems with discrete time-delays, both delay-independent stability conditions and delay-dependent stability conditions have already been obtained. However, no stability condition for fuzzy systems with distributed time-delays has appeared in the literature. This is also true in case of the robust stability for uncertain fuzzy systems with distributed time-delays. With the aid of the stability theorems of linear systems with distributed time-delays, we employ a similar Lyapunov functional for the stability of fuzzy time-delay systems. Then we introduce many free matrices to such a Lyapunov functional, in order to obtain delay-dependent stability conditions. These techniques lead to generalized and less conservative stability conditions. In fact, delay-dependent stability conditions thus obtained are given in linear matrix inequalities(LMIs) and guarantee a wide stability region. We also consider the robust stability of fuzzy time-delay systems with uncertain parameters. Applying the same techniques made on the stability conditions, we obtain delay-dependent sufficient conditions for the robust stability of uncertain fuzzy systems with discrete and distributed time-delays. Moreover, we consider the state feedback stabilization. Based on stability and robust stability conditions, we obtain conditions for the state feedback controller to stabilize the fuzzy time-delay systems. Finally, we take some examples to illustrate our results.

One of the actual problems for the theory and practice of control of dynamic objects is the development of methods for research and synthesis of control systems of multidimensional objects. The paper proposes a universal approach to construct Lyapunov vector functions directly from the equation of state of control system and a new gradient-speed method of Lyapunov vector functions to study aperiodic robust stability of linear control system with m inputs and n outputs. The study of aperiodic robust stability of automatic control systems is based on the construction of Lyapunov vector functions and gradient-speed dynamic control systems. The basic statements of Lyapunov's theorem about asymptotic stability and notions of stability of dynamic systems are used. The representation of control systems as gradient systems and Lyapunov functions as potential functions of gradient systems from the catastrophe theory allow to construct the full-time derivative of Lyapunov vector functions always as a sign-negative function equal to the scalar product of the velocity vector on the gradient vector. The conditions of aperiodic robust stability are obtained as a system of inequalities on the uncertain parameters of the automatic control system, which are a condition for the existence of the Lyapunov vector-function. A numerical example of synthesis of aperiodic robustness of a multidimensional control object is given. The example shows the main stages of the developed synthesis method, the study of the system stability at different values of the coefficients k, confirming the consistency of the proposed method. Transients in the system satisfy all requirements

This paper overviews the research investigations pertaining to stability and stabilization of control systems with time‐delays. The prime focus is the fundamental results and recent progress in theory and applications. The overview sheds light on the contemporary development on the linear matrix inequality (LMI) techniques in deriving both delay‐independent and delay‐dependent stability results for time‐delay systems. Particular emphases will be placed on issues concerned with the conservatism and the computational complexity of the results. Key technical bounding lemmas and slack variable introduction approaches will be presented. The results will be compared and connections of certain delay‐dependent stability results are also discussed.

The accuracy of a digital filter is limited by the finite word length used in its implementation. Techniques have been developed to analyze this problem. Good agreement between the theoretical and experimental results has been reported. This paper discusses some of these accuracy problems and reviews some of the approaches used in investigating them. The calculation of the statistical mean-squared error at the output of the filter is discussed in detail.

Comments on 'Effects of finite word length on FIR filters for MTD processing' by the author of 'Sacrifices in radar clutter suppression due to compromises in implementation of digital Doppler filters'

Adaptive FIR filters are important in modern digital signal processing applications, and many situations require significant computational power attainable only through multi-processor configurations. Various block processing techniques have been proposed as viable alternatives to the sequential implementations to achieve the high throughput rate and reduce the effect of finite word length. While there are algorithm-based fault-tolerant techniques for protecting general digital signal processing systems against temporary/permanent failures, the specific features and requirements of the adaptive filtering systems have been largely ignored in the fault tolerance literature. By identifying common operations among different block adaptive filtering algorithms, however most operations of a particular algorithm can be protected with reasonably low-cost. We present a fine-grained approach, a highly efficient implementation of the well-known checksum encoding scheme, for protecting block adaptive filters. Through properly partitioning the input data, checksums for a parallel adaptive FIR filter can be calculated with reduced complexity. Computational and hardware overhead of the proposed scheme are analyzed, and shown to be proportional to the total number of partitioned submatrices.

Stability and steady state analysis of control and safety systems of Nuclear Power Plants

In this paper, we consider the problems of robust stability and stabilization of Lurpsilae control systems with time-varying delay. Firstly, by making use of an integral inequality, some delay-dependent robust stability conditions of the system are presented. Then, a sufficient stabilization criterion is established in the terms of linear matrix inequality (LMI), based on the above stability condition and matrix decomposition technique. Finally, numerical examples are given to illustrate the effectiveness of the proposed results.

The effect of the finite word length on the moment of the impulse response of a digital filter is investigated. It is shown that the quantization error in the moment values is almost linear with a slope of 3 dB/b and is well related to the output roundoff noise. An algorithm is also proposed to order the cascade sections of a finite impulse response (FIR) filter with low output roundoff noise. >