This paper studies a number of quantized feedback design problems for linear systems. We consider the case where quantizers are static (memoryless). The common aim of these design problems is to stabilize the given system or to achieve certain performance with the coarsest quantization density. Our main discovery is that the classical sector bound approach is nonconservative for studying these design problems. Consequently, we are able to convert many quantized feedback design problems to well-known robust control problems with sector bound uncertainties. In particular, we derive the coarsest quantization densities for stabilization for multiple-input-multiple-output systems in both state feedback and output feedback cases; and we also derive conditions for quantized feedback control for quadratic cost and H/sub /spl infin// performances.

The sector bound approach to quantized feedback control | NOVA. The University of Newcastle's Digital Repository

During the last decade, a big progress has been achieved in the analysis and numerical treatment of Initial Value Problems (IVPs) in Differential Algebraic Equations (DAEs) and Ordinary Differential Equations (ODEs). In spite of the rich variety of results available in the literature, there are still many specific problems that require special attention. Two of such, which are considered in this work, are the optimization of order of accuracy and reduction of cost of functional evaluations of Explicit Runge - Kutta (ERK) methods.

Traditionally, the maximum attainable order p of an s-stage ERK method for advancing the solution of an IVP is such that
p(s)
 4
 
In 1999, Goeken presented an s-stage ERK Method of order p(s)=s +1,s>2.
However, this work focuses on the design of a new approximation algorithm that reduces the cost of functional evaluations and yet increases the attainable order higher 
U n and Jonhson [94]; and the classical ERK methods. The order p of 
the new scheme called Multiderivative Explicit Runge-Kutta (MERK) Methods is such that p(s) 2. The stability, convergence and implementation for the optimization of IVPs in DAEs and ODEs systems are also considered.

Numerical solution of initial value problems in differential - algebraic equations

The work is giving estimations of the discrepancy between solutions of the initial and the homogenized problems for a one{dimensional second order elliptic operators with random coeecients satisfying strong or uniform mixing conditions. We obtain several sharp estimates in terms of the corresponding mixing coeecient. Abstract. In the theory of homogenisation it is of particular interest to determine the classes of problems which are stable on taking the homogenisation limits. A notable situation where the limit enlarges the class of original problems is known as memory (nonlocal) eeects. A number of results in that direction has been obtained for linear problems. Tartar (1990) innitiated the study of the eeective equation corresponding to nonlinear equation: @ t u n + a n u 2 n = f: Signiicant progress has been hampered by the complexity of required computations needed in order to obtain the terms in power{series expansion. We propose a method which overcomes that diiculty by introducing graphs representing the domain of integration of the integrals in each term. The graphs are relatively simple, it is easy to calculate with them and they give us a clear image of the form of each term. The method allows us to discuss the form of the eeective equation and the convergence of power{series expansions. The feasibility of our method for other types of nonlinearities will be discussed as well.

Applied Mathematics and Computation

In this paper we discussed delay-dependent feedback stabilization of linear uncertain state-delayed systems. Based on the status feedback of system, the control regularity for the feedback stability of system is offered. Using the linear matrix inequality (LMI), we got the sufficient condition for the feedback stability of system. Finally an illustrative example verified the effectiveness and rationality of the conclusion.

Delay-Dependent Robust Stabilization of Uncertain State-Delayed Systems

This paper investigates the problem of the sampled-data extended dissipative control for uncertain Markov jump systems. The systems considered are transformed into Markov jump systems with polytopic uncertainties and sawtooth delays by using an input delay approach. The focus is on the design of a mode-independent sampled-data controller such that the resulting closed-loop system is mean-square exponentially stable with a given decay rate and extended dissipative. A novel exponential stability criterion and an extended dissipativty condition are established by proposing a new integral inequality. The reduced conservatism of the criteria is demonstrated by two numerical examples. Furthermore, a sufficient condition for the existence of a desired mode-independent sampled-data controller is obtained by solving a convex optimisation problem. Finally, a resistance, inductance and capacitance (RLC) series circuit is employed to illustrate the effectiveness of the proposed approach.

Robust extended dissipative control for sampled-data Markov jump systems

Stabilization of singular Markovian jump systems with time-varying switchings

This monograph is an up-to-date presentation of the analysis and design of singular Markovian jump systems (SMJSs) in which the transition rate matrix of the underlying systems is generally uncertain, partially unknown and designed. The problems addressed include stability, stabilization, H? control and filtering, observer design, and adaptive control. applications of Markov process are investigated by using Lyapunov theory, linear matrix inequalities (LMIs), S-procedure and the stochastic Barbalat’s Lemma, among other techniques.

Features of the book include:

· study of the stability problem for SMJSs with general transition rate matrices (TRMs);

· stabilization for SMJSs by TRM design, noise control, proportional-derivative and partially mode-dependent control, in terms of LMIs with and without equation constraints;

· mode-dependent and mode-independent H? control solutions with development of a type of disordered controller;

· observer-based controllers of SMJSs in which both the designed observer and controller are either mode-dependent or mode-independent;

· consideration of robust H? filtering in terms of uncertain TRM or filter parameters leading to a method for totally mode-independent filtering

· development of LMI-based conditions for a class of adaptive state feedback controllers with almost-certainly-bounded estimated error and almost-certainly-asymptotically-stable corresponding closed-loop system states

· applications of Markov process on singular systems with norm bounded uncertainties and time-varying delays

Analysis and Design of Singular Markovian Jump Systems contains valuable reference material for academic researchers wishing to explore the area. The contents are also suitable for a one-semester graduate course.

Analysis and Design of Singular Markovian Jump Systems

This study focuses on the problem of robust control for a class of uncertain singular stochastic Markovian jump systems via proportional-derivative state feedback controllers (PDSFCs). The uncertainties are not only in system matrices, such as state, input and derivative matrices, but also in mode transition rate matrix. New sufficient conditions for the existence of mode-dependent PDSFC are derived as linear matrix inequalities (LMIs) such that the closed-loop singular stochastic system is quadratically normal and quadratically stochastically stable (QNQSS). Especially, another PDSFC referred to be partially mode dependent is also given by a mode-dependent Lyapunov function. Numerical examples are used to show the effectiveness of the proposed methods.

Robust control of uncertain singular stochastic systems with Markovian switching via proportional–derivative state feedback

SUMMARY

This paper is concerned with the H ∞  filter design for continuous-time singular systems with Markovian jump parameters, whose system mode is transmitted through an unreliable network. In contrast to the traditionally mode-dependent or mode-independent filtering method, a new partially mode-dependent filter is established via using a mode-dependent Lyapunov function, where the stochastic property of mode available to a filter is considered. Sufficient conditions for the existence of H ∞  filter are obtained as strict linear matrix inequalities. Finally, numerical examples are used to show the effectiveness of the given theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.

Guoliang Wang

Papers

Stabilization of singular Markovian jump systems with time-varying switchings

Analysis and Design of Singular Markovian Jump Systems

Robust control of uncertain singular stochastic systems with Markovian switching via proportional–derivative state feedback

Exponential H ∞ filtering for singular systems with Markovian jump parameters

Robust finite-time stability and stabilization of uncertain Markovian jump systems with time-varying delay