Abstract
In this chapter we have considered linear systems subject to parametric uncertainties. The quadratic stabilization problem can be solved in an elegant way, via convex optimization procedures, if the dependence of the system matrices on parameters is the ratio of multiaffine polynomials. In the other cases we can use an algorithm which, under mild assumptions, transforms a given nonlinear matrix function into a multiaffine one. Via this algorithm and at the price of some conservatism, we can solve the quadratic stabilization problem referred to a fictitous system depending multiaffinely on parameters. An algorithm to reduce such conservatism has also been presented.
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Amato, F., Garofalo, F., Glielmo, L., Pironti, A. (1996). Quadratic stabilization of uncertain linear systems. In: Garofalo, F., Glielmo, L. (eds) Robust Control via Variable Structure and Lyapunov Techniques. Lecture Notes in Control and Information Sciences, vol 217. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0027567
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DOI: https://doi.org/10.1007/BFb0027567
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