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Recently, probabilistic methods and statistical learning theory have been shown to provide approximate solutions to \diicult" control problems. Unfortunately, the number of samples required (based on VC-dimension results) in order to guarantee stringent performance levels may be prohibitively large. This paper introduces bootstrap learning methods and the(More)
This paper shows how certain robust multi-objective feedback design problems can be reduced to quantifier elimination (QE) problems. In particular it is shown how robust stabilization and robust frequency domain performance specifications can be reduced to systems of polynomial inequalities with suitable logic quantifiers, ∀ and ∃. Because of computational(More)
This paper reviews the static output feedback problem in the control of linear, time-invariant (LTI) systems. It includes analytical and computational methods and presents in a unified fashion, the knowledge gained in the decades of research into this important open problem. The paper shows that although many approaches and techniques exist to approach(More)
In this paper we show how a number of interesting linear control system analysis and design problems can be reduced to Quantiier Elimination (QE) problems. We assume a xed structure for the compensator, with design parameters q i. The problems considered are problems that currently have no general solution. However, the problems must be of modest complexity(More)
This paper describes the synthesis of non-fragile or resilient regulators for linear systems. A general framework for fragility is described using state-space methodologies, and the LQ/H 2 static state-feedback problem is examined in detail. We discuss the multiplicative structured uncertainties case, and propose remedies of the fragility problem using an(More)