Analysis of Implicit Uncertain Systems. Part II: Constant Matrix Problems and Application to Robust H2 Analysis

This paper introduces an implicit framework for the analysis of uncertain systems, of which the general properties were described in Part I. In Part II, the theory is specialized to problems which admit a finite dimensional formulation. A constant matrix version of implicit analysis is presented, leading to a generalization of the structured singular value μ as the stability measure; upper bounds are developed and analyzed in detail. An application of this framework results in a practical method for robust H2 analysis: computing robust performance in the presence of norm-bounded perturbations and white-noise disturbances

Robustness analysis of magnetic torquer controlled spacecraft attitude dynamics

This paper describes a systematic approach to the robustness analysis of linear periodically time-varying (LPTV) systems. The method uses the technique known as Lifting to transform the original time-varying uncertain system into linear fractional transformation (LFT) form. The stability and performance robustness of the system to structured parametric uncertainty can then be analysed non-conservatively using the structured singular value μ. The method is applied to analyse the stability robustness of an attitude control law for a spacecraft controlled by magnetic torquer bars, whose linearised dynamics can naturally be written in linear periodically time-varying form. The proposed method allows maximum allowable levels of uncertainty, as well as worst-case uncertainty combinations to be computed. The destabilising effect of these uncertain parameter combinations is verified in time-domain simulations

Sets and Constraints in the Analysis Of Uncertain Systems

This thesis is concerned with the analysis of dynamical systems in the presence of model uncertainty. The approach of robust control theory has been to describe uncertainty in terms of a structured set of models, and has proven successful for questions, like stability, which call for a worst-case evaluation over this set. In this respect, a first contribution of this thesis is to provide robust stability tests for the situation of combined time varying, time invariant and parametric uncertainties. The worst-case setting has not been so attractive for questions of disturbance rejection, since the resulting performance criteria (e.g., ℋ∞,) treat the disturbance as an adversary and ignore important spectral structure, usually better characterized by the theory of stochastic processes. The main contribution of this thesis is to show that the set-based methodology can indeed be extended to the modeling of white noise, by employing standard statistical tests in order to identify a typical set, and performing subsequent analysis in a worst-case setting. Particularly attractive sets are those described by quadratic signal constraints, which have proven to be very powerful for the characterization of unmodeled dynamics. The combination of white noise and unmodeled dynamics constitutes the Robust ℋ2 performance problem, which is rooted in the origins of robust control theory. By extending the scope of the quadratic constraint methodology we obtain a solution to this problem in terms of a convex condition for robustness analysis, which for the first time places it on an equal footing with the ℋ∞ performance measure. A separate contribution of this thesis is the development of a framework for analysis of uncertain systems in implicit form, in terms of equations rather than input-output maps. This formulation is motivated from first principles modeling, and provides an extension of the standard input-output robustness theory. In particular, we obtain in this way a standard form for robustness analysis problems with constraints, which also provides a common setting for robustness analysis and questions of model validation and system identification

Analysis and design of multirate-multivariable sampled data systems

Imperial Users onl

Aeronautical engineering: A continuing bibliography with indexes (supplement 275)

This bibliography lists 379 reports, articles, and other documents introduced into the NASA scientific and technical information system in Jan. 1991

ロバスト性解析と制御器設計のための離散時間非因果的周期時変スケーリング

京都大学0048新制・課程博士博士(工学)甲第17889号工博第3798号新制||工||1581(附属図書館)30709京都大学大学院工学研究科電気工学専攻(主査)教授 萩原 朋道, 教授 土居 伸二, 准教授 久門 尚史学位規則第4条第1項該当Doctor of Philosophy (Engineering)Kyoto UniversityDFA

Robust Observer-Based Output Feedback Control of a Nonlinear Time-Varying System

A class of time-varying systems can be quadratically stabilized with satisfactory performance by a modified time-invariant-based observer. The modified observer driven by the additional adaptation forces with static correction gains is used to estimate the time-varying system states. Under the frame of quadratic stability, the closed-loop systems satisfying induced norm bounded performance criterion are exponentially stabilized while the states are exponentially approaching by the modified observer. This paper deals with the time-varying systems that can be characterized as the multiplicative type of time-invariant and time-varying parts. The time-invariant part is then used to construct the modified observer with additional driving forces, which are ready to adjust time-varying effect coming from the measured outputs feeding into the modified observer. The determination of the adaptation forces can be derived from the minimization of the cost of error dynamics with modified least-squares algorithms. The synthesis of control and observer static correction gains are also demonstrated. The developed systems have been tested in a mass-spring-damper system to illustrate the effectiveness of the design