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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)
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 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)
It has recently become clear that many control problems are too dicult to admit analytic solutions. New results have also emerged to show that the computational complexity of somè`solved'' control problems is prohibitive. Many of these control problems can be reduced to decidability problems or to optimization questions. Even though such questions may be(More)
In this brief paper we present sufficient conditions for the existence of a single stable controller to stabilize a set of n As is well known this is equivalent to the existence of a single controller, not necessarily stable, to stabilize n + 1 plants (simultaneous stabilization). The basic assumption required in the current paper is that all the plants(More)