Lihua Xie

Output feedback H∞ control of systems with parameter uncertainty

This paper deals with H ∞ control problem for systems with parametric uncertainty in all matrices of the system and output equations. The parametric uncertainty under consideration is of a linear fractional form. Both the continuous and the discrete-time cases are considered. Necessary and sufficient conditions for quadratic stability with H ∞ disturbance attenuation are obtained.

Robust control of a class of uncertain nonlinear systems

This paper considers the robust control of a class of nonlinear systems with real time-varying parameter uncertainty. Interest is focused on the design of linear dynamic output feedback control and two problems are addressed. The first one is the robust stabilization and the other is the problem of robust performance in an H∞ sense. A technique is proposed for designing stabilizing controllers for both problems by converting them into ‘scaled’ H∞ control problems which do not involve parameter uncertainty.

The sector bound approach to quantized feedback control

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.

Further Improvement of Free-Weighting Matrices Technique for Systems With Time-Varying Delay

A novel method is proposed in this note for stability analysis of systems with a time-varying delay. Appropriate Lyapunov functional and augmented Lyapunov functional are introduced to establish some improved delay-dependent stability criteria. Less conservative results are obtained by considering the additional useful terms (which are ignored in previous methods) when estimating the upper bound of the derivative of Lyapunov functionals and introducing the new free-weighting matrices. The resulting criteria are extended to the stability analysis for uncertain systems with time-varying structured uncertainties and polytopic-type uncertainties. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

Robust Kalman filtering for uncertain discrete-time systems

This paper is concerned with the problem of a Kalman filter design for uncertain discrete-time systems. The system under consideration is subjected to time-varying norm-bounded parameter uncertainty in both the state and output matrices. The problem addressed is the design of a linear filter such that the variance of the filtering error is guaranteed to be within a certain bound for all admissible uncertainties. Furthermore, the guaranteed cost can be optimized by appropriately searching a scaling design parameter. >

New approach to mixed H/sub 2//H/sub /spl infin// filtering for polytopic discrete-time systems

This paper revisits the problem of mixed H/sub 2//H/sub /spl infin// filtering for polytopic discrete-time systems. Differing from previous results in the quadratic framework, the filter design makes full use of the parameter-dependent stability idea: Not only is the filter dependent of the parameters (which are assumed to reside in a polytope and be measurable online), but in addition, the Lyapunov matrices are different for the entire polytope domain, as well as for different channels with respect to the mixed performances. These ideas are realized by introducing additional slack variables to the well-established performance conditions and by employing new bounding techniques, which results in a much less conservative filter design method. A numerical example is presented to illustrate the effectiveness and advantage of the developed filter design method.

Improved robust H2 and H∞ filtering for uncertain discrete-time systems

A process for producing toner particles for developing electrostatic latent images, comprising the steps of introducing colored solid particles containing a binder resin into a multi-division classifying zone divided into at least three sections by partitioning means, so that the particles are fallen along curved lines; collecting a coarse powder consisting primarily of coarse particles in a first divided section, a medium powder consisting primarily of particles having a particle size within a defined range in a second divided section and a fine powder consisting primarily of particles having a particle size smaller than the defined range in a third divided section; feeding the classified coarse powder to a pulverizing step; and introducing the pulverized powder into the multi-division classifying zone. An apparatus for practicing the process is also disclosed.

Distributed Consensus With Limited Communication Data Rate

Communication data rate and energy constraints are important factors which have to be considered when investigating distributed coordination of multi-agent networks. Although many proposed average-consensus protocols are available, a fundamental theoretic problem remains open, namely, how many bits of information are necessary for each pair of adjacent agents to exchange at each time step to ensure average consensus? In this paper, we consider average-consensus control of undirected networks of discrete-time first-order agents under communication constraints. Each agent has a real-valued state but can only exchange symbolic data with its neighbors. A distributed protocol is proposed based on dynamic encoding and decoding. It is proved that under the protocol designed, for a connected network, average consensus can be achieved with an exponential convergence rate based on merely one bit information exchange between each pair of adjacent agents at each time step. An explicit form of the asymptotic convergence rate is given. It is shown that as the number of agents increases, the asymptotic convergence rate is related to the scale of the network, the number of quantization levels and the ratio of the second smallest eigenvalue to the largest eigenvalue of the Laplacian of the communication graph. We also give a performance index to characterize the total communication energy to achieve average consensus and show that the minimization of the communication energy leads to a tradeoff between the convergence rate and the number of quantization levels.

Network Topology and Communication Data Rate for Consensusability of Discrete-Time Multi-Agent Systems

This paper investigates the joint effect of agent dynamic, network topology and communication data rate on consensusability of linear discrete-time multi-agent systems. Neglecting the finite communication data rate constraint and under undirected graphs, a necessary and sufficient condition for consensusability under a common control protocol is given, which explicitly reveals how the intrinsic entropy rate of the agent dynamic and the communication graph jointly affect consensusability. The result is established by solving a discrete-time simultaneous stabilization problem. A lower bound of the optimal convergence rate to consensus, which is shown to be tight for some special cases, is provided as well. Moreover, a necessary and sufficient condition for formationability of multi-agent systems is obtained. As a special case, the discrete-time second-order consensus is discussed where an optimal control gain is designed to achieve the fastest convergence. The effects of undirected graphs on consensability/formationability and optimal convergence rate are exactly quantified by the ratio of the second smallest to the largest eigenvalues of the graph Laplacian matrix. An extension to directed graphs is also made. The consensus problem under a finite communication data rate is finally investigated.

Brief paper: Optimal linear estimation for systems with multiple packet dropouts

This paper is concerned with the optimal linear estimation problem for linear discrete-time stochastic systems with multiple packet dropouts. Based on a packet dropout model, the optimal linear estimators including filter, predictor and smoother are developed via an innovation analysis approach. The estimators are computed recursively in terms of the solution of a Riccati difference equation of dimension equal to the order of the system state plus that of the measurement output. The steady-state estimators are also investigated. A sufficient condition for the convergence of the optimal linear estimators is given. Simulation results show the effectiveness of the proposed optimal linear estimators.