Huaizhong Li

Passivity analysis and passification for uncertain signal processing systems

The problem of passivity analysis finds important applications in many signal processing systems such as digital quantizers, decision feedback equalizers, and digital and analog filters. Equally important is the problem of passification, where a compensator needs to be designed for a given system to become passive. This paper considers these two problems for a large class of systems that involve uncertain parameters, time delays, quantization errors, and unmodeled high-order dynamics. By characterizing these and many other types of uncertainty using a general tool called integral quadratic constraints (IQCs), we present solutions to the problems of robust passivity analysis and robust passification. More specifically, for the analysis problem, we determine if a given uncertain system is passive for all admissible uncertainty satisfying the IQCs. Similarly, for the problem of robust passification, we are concerned with finding a loop transformation such that a particular part of the uncertain signal processing system becomes passive for all admissible uncertainty. The solutions are given in terms of the feasibility of one or more linear matrix inequalities (LMIs), which can be solved efficiently.

Delay-dependent closed-loop stability of linear systems with input delay: an LMI approach

This paper focuses on the problem of computing a control law which maximizes (in a sub-optimal sense) the delay of the closed-loop system for a class of linear systems with delayed input. The delay is assumed to be a continuous bounded time-varying function. The analysis is given using two different approaches: the Razumikhin based method and a frequency-filtering based method.

Robust /spl Hscr//sub /spl infin// control of uncertain linear time-delay systems: a linear matrix inequality approach. I

This paper is concerned with the robust /spl Hscr//sub /spl infin// control problem of uncertain linear time-delay systems using a linear matrix inequality approach. The uncertainty described in this paper is in the quadratic constraint form, which takes some well-known uncertainty descriptions as special examples. Four specific problems are tackled, namely the robust /spl Hscr//sub /spl infin// analysis problem, the robust /spl Hscr//sub /spl infin// control problem using memoryless static state feedback, the robust /spl Hscr//sub /spl infin// control problem using memoryless dynamic state feedback and the /spl Hscr//sub /spl infin// control using memoryless static output feedback. We show that feasibility of some LMIs guarantees the solvability of the corresponding problem.

Robust guaranteed cost control for uncertain linear time-delay systems

This paper is concerned with robust guaranteed cost control for uncertain linear time-delay systems with quadratically constrained uncertainty using a linear matrix inequality (LMI) approach. The quadratically constrained uncertainty described in this paper is general in nature and takes some well-known uncertainty descriptions as special cases. Two specific problems are considered in this paper, namely the robust guaranteed cost control problem using memoryless static state feedback and the one using memoryless static output feedback. We show that feasibility of some LMIs guarantees the solvability of the corresponding robust guaranteed cost control problem.

Passivity analysis for uncertain signal processing systems

The problem of passivity analysis finds important applications in many signal processing systems such as digital quantizers, decision feedback equalizers and digital and analog filters. This paper considers the passivity analysis problem for a large class of systems which involve uncertain parameters, time delays, quantization errors, and unmodeled high order dynamics. By characterizing these and many other types of uncertainty using a general tool called integral quadratic constraints (IQCs), we present a solution to the problem of robust passivity analysis. More specifically, we determine if a given uncertain system is robustly passive. The solution is given in terms of the feasibility of a linear matrix inequality (LMI) which can be solved efficiently.

Model Following Robust Control of Linear Time-Varying Uncertain Systems

This paper considers the problem of model following robust control of linear time-varying single-input single-output uncertain systems. Under some mild assumptions, we show that a minimum-phase uncertain system with known order and known relative degree can be controlled to achieve both robust stability and arbitrarily good model following performance by using a simple linear time invariant controller. The controller is of two-degree-of-freedom which involves prefiltering and high gain feedback compensation. The uncertainties in the system are allowed to be very large sizes with large rates of change. Our result generalizes similar results for linear and nonlinear time invariant systems.

Generalized Popov Theory Applied to State-Delayed Systems

Abstract The paper is dealing with the generalized Popov theory applied to state-delayed systems. Sufficient conditions for stabilizing time-delay systems as well as for coerciveness of an appropriate quadratic cost are given.

Robust Guaranteed Cost Control of Uncertain Linear Time-Delay Systems with Mixed State and Input Delays

This paper is concerned with robust guaranteed cost control for uncertain linear time-delay systems with state delay, input delay and quadratically constrained uncertainty using a linear matrix inequality (LMI) approach. The quadratically constrained uncertainty described in this paper is general in nature and takes some well-known uncertainty descriptions as special cases. We only consider the memoryless static state feedback in this paper. We show that feasibility of some LMIs guarantees the solvability of the corresponding robust guaranteed cost control problem.

Control of Large Scale Linear Delay Systems Using Generalized Popov Theory

Abstract The paper deals with the generalized Popov theory applied to large scale-delayed systems. Sufficient conditions for stabilizing large scale-delayed systems as well as for γ- attenuation achievement are given in terms of algebraic properties of a Popov system via a Liapunov - Krasovskii functional. The considered approach, successfully applied to classical linear systems, is new in the context of large scale linear-delay systems and gives some interesting interpretations of H∞ memoryless control problems in terms of Popov triplets and associated objects.

Constrained robust guaranteed cost control for uncertain linear time-delay system

This paper is concerned with constrained robust guaranteed cost control for uncertain linear time-delay systems using a linear matrix inequality (LMI) approach. Provided with necessary conditions, the problem considered is to design a static state feedback controller for a class of linear uncertain time-delay systems such that the following three goals are achieved simultaneously: 1) the closed-loop systems with this controller are robustly stable; 2) a given quadratic performance index for the systems is guaranteed to be below a known upper bound; and 3) the control input is norm bounded. We show that the solvability of the addressed problem is implied by the feasibility of some linear matrix inequalities.