Kemin Zhou

Robust stabilization of uncertain linear systems: quadratic stabilizability and H/sup infinity / control theory

The problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time-domain results on the quadratic stabilization of uncertain systems and the frequency-domain results on H/sup infinity / optimization. A complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given. Relations between these robust stabilization problems and H/sup infinity / control theory are explored. It is also shown that in a number of cases, if a robust stabilization problem can be solved via Lyapunov methods, then it can be also be solved via H/sup infinity / control theory-based methods. >

An algebraic Riccati equation approach to H ∞ optimization

Abstract This paper considers the general (so-called four block) H ∞ optimal control problem with the assumption that system states are available for feedback. It is shown that infimization of the H ∞ norm of the closed loop transfer function over all linear constant, i.e., nondynamic, stabilizing state feedback laws can be completely characterized via an algebraic Riccati equation. It is further shown that the optimal norm is not improved by allowing feedback to be dynamic. Thus, the general state-feedback H ∞ optimal control problem can be solved by iteratively solving one ARE and the controller can be chosen to be static gain.

Robust stabilization of linear systems with norm-bounded time-varying uncertainty

Abstract In this paper, robust stabilization of a class of linear systems with norm-bounded time-varying uncertainties is considered. It is shown that for this class of uncertain systems quadratic stabilizability via linear control is equivalent to the existence of a positive definite symmetric matrix solution to a (parameter-dependent) Riccati equation. Also, a construction for the stabilizing feedback law is given in terms of the solution to the Riccati equation.

Stability robustness bounds for linear state-space models with structured uncertainty

In this note, we consider the robust stability analysis problem in linear state-space models. We consider systems with structured uncertainty. Some lower bounds on allowable perturbations which maintain the stability of a nominally stable system are derived. These bounds are shown to be less conservative than the existing ones.

Review of LFTs, LMIs, and mu

The authors present a tutorial overview of linear fractional transformations (LFTs) and the role of the structured singular value, mu , and linear matrix inequalities (LMIs) in solving LFT problems. The authors first introduce the notation for LFTs and briefly discuss some of their properties. They then describe mu and its connections with LFTs. They focus on two standard notions of robust stability and performance, mu stability and performance and Q stability and performance, and their relationship is discussed. Comparisons with the L/sub 1/ theory of robust performance with structured uncertainty are considered.<<ETX>>

A new controller architecture for high performance, robust, and fault-tolerant control

We propose a new feedback controller architecture. The distinguished feature of our new controller architecture is that it shows structurally how the controller design for performance and robustness may be done separately which has the potential to overcome the conflict between performance and robustness in the traditional feedback framework. The controller architecture includes two parts: one part for performance and the other part for robustness. The controller architecture works in such a way that the feedback control system can be solely controlled by the performance controller when there is no model uncertainties and external disturbances and the robustification controller can only be active when there are model uncertainties or external disturbances.

Detection, estimation, and accommodation of loss of control effectiveness

In this paper, an adaptive Kalman filtering algorithm is developed for use to estimate the reduction of control effectiveness in a closed-loop setting. Control effectiveness factors are used to quantify faults entering control systems through actuators. A set of covariance-dependent forgetting factors is introduced into the filtering algorithm. As a result, the change in the control effectiveness is accentuated to help achieve a more accurate estimate more rapidly. A weighted sum-squared bias estimate is defined for the change detection. The state estimate is fed back to achieve the steady-state regulation, while the control effectiveness estimate is used for the on-line tuning of the control law. A stability analysis is performed for the adaptive regulator. Copyright

Mixed /spl Hscr//sub 2/ and /spl Hscr//sub /spl infin// performance objectives. II. Optimal control

This paper considers the analysis and synthesis of control systems subject to two types of disturbance signals: white signals and signals with bounded power. The resulting control problem involves minimizing a mixed /spl Hscr//sub 2/ and /spl Hscr//sub /spl infin// norm of the system. It is shown that the controller shares a separation property similar to those of pure /spl Hscr//sub 2/ or /spl Hscr//sub /spl infin// controllers. Necessary conditions and sufficient conditions are obtained for the existence of a solution to the mixed problem. Explicit state-space formulas are also given for the optimal controller. >

Mixed /spl Hscr//sub 2/ and /spl Hscr//sub /spl infin// performance objectives. I. Robust performance analysis

This paper introduces an induced-norm formulation of a mixed /spl Hscr//sub 2/ and /spl Hscr//sub /spl infin// performance criterion. It is shown that different mixed /spl Hscr//sub 2/ and /spl Hscr//sub /spl infin// norms arise from different assumptions on the input signals. While most mixed norms can be expressed explicitly using either transfer functions or state-space realizations of the system, there are cases where the explicit formulas are very hard to obtain. In the later cases, examples are given to show the intrinsic nature and difficulty of the problem. Mixed norm robust performance analysis under structured uncertainty is also considered in the paper. >

On the weighted sensitivity minimization problem for delay systems

We consider the H∞-optimal sensitivity problem for delay systems. In particular, we consider computation of μ:= inf {|W-φq|∞ : q ϵ H∞(jR)} where W(s) is any function in RH∞(jR), and φ in H∞(jR) is any inner function. We derive a new explicit solution in the pure delay case where φ = e−sh, h > 0.