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Control of Uncertain Systems: State-Space Characterizations


Lu, Wei-Min (1995) Control of Uncertain Systems: State-Space Characterizations. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/dnxg-nz58.


A central issue in control system design has been to deal with uncertainty and nonlinearity in the systems. In this dissertation, an integrated treatment for both uncertainty and nonlinearity is proposed. This dissertation consists of two relatively independent parts. The first part deals with uncertain linear systems, while the second part treats uncertain nonlinear systems.

In the first part, the problem of control synthesis of uncertain linear systems is considered. A linear fractional transformation (LFT) framework is proposed for robust control design of uncertain linear control systems with structured uncertainty. Linear parameter-varying systems whose coefficients depend on some time-invariant unknown parameters are treated in a general algebraic framework; both the stabilization and the H-control problems are considered. For uncertain linear systems under structured perturbations, robustness synthesis problems are characterized in terms of linear matrix inequalities (LMIs) in the LFT framework. A generalized PBH test is also used to characterize the robustness synthesis problems. Moreover, a separation principle for the control synthesis of uncertain linear systems is revealed. The machinery also streamlines a number of results concerning the analysis and synthesis of multidimensional systems.

In the second part, the problem of control synthesis for nonlinear systems is addressed; stabilization, L1-control, H-control, robustness analysis, and robustness synthesis problems for nonlinear systems are examined in detail. In particular, locally and globally stabilizing controller parameterizations for nonlinear systems are derived; the formulae generalize the celebrated Youla-parameterization for linear systems. Both nonlinear L1-control and nonlinear H-control are also considered for dealing with disturbance attenuation problems for nonlinear systems. The L1-performance and L1-control of nonlinear systems are characterized in terms of certain invariance sets of the state space; in addition, the relation between the L1-control of a continuous-time system and the ℓ1-control of the related Euler approximated discrete-time systems is established. A systematic treatment for H-control synthesis of nonlinear systems is provided; the nonlinear H-control problem is characterized in terms of Hamilton-Jacobi Inequalities (HJIs) and nonlinear matrix inequalities (NLMIs); a class of H-controllers are parameterized as a fractional transformation of contractive stable parameters. Finally, the problems of stability and performance robustness analysis and synthesis for uncertain nonlinear systems subject to structured perturbations with bounded L2-gains are introduced; they are characterized in terms of HJIs and NLMIs as well. Computational issues are also addressed; it is confirmed that the computation needed for robustness analysis and synthesis of nonlinear systems is of equivalent difficulty to that for checking Lyapunov stability.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Electrical Engineering and Mathematics)
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Electrical Engineering
Minor Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Doyle, John Comstock
Thesis Committee:
  • Doyle, John Comstock (chair)
  • Hou, Thomas Y.
  • Murray, Richard M.
  • Perona, Pietro
  • Wiggins, Stephen R.
Defense Date:8 March 1995
Record Number:CaltechETD:etd-03022006-131646
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:835
Deposited By: Imported from ETD-db
Deposited On:03 Mar 2006
Last Modified:30 Aug 2022 21:18

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