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 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 uniied fashion, the knowledge gained in the decades of research into this most important problem.
This paper presents a new approach to the synthesis of stabilizing controllers for a class of one-parameter interval plants. The approach is based on the concept of analytic-real-positive (ARP) functions.
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 dicult 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 paper the stability analysis of nonlinear systems is studied through different approaches. The main idea of the paper is to map the original class of nonlinear systems into a smaller subclass of systems described by multivariate polynomial functions, for which the study of stability is available.
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)