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A stabilization algorithm for a class of uncertain linear systems. (English) Zbl 0618.93056
Necessary and sufficient conditions are given for the quadratic stabilization of the uncertain control system \[ \dot x(t)=(A+DF(t)E)x(t)+Bu(t),\quad F^ T(t)F(t)\leq I, \] \(x\in {\mathfrak R}^ n\), \(u\in {\mathfrak R}^ m\), and \(F\in {\mathfrak R}^{p\times q}\). The form of the stabilizing feedback control is \(u^*(t)=-R^{-1}B^ TPx(t)\), where R and P are positive definite matrices of appropriate dimension, and P solves an algebraic Riccati equation. It is demonstrated that with the notion of ”overbounding”, it is possible to use the control law \(u^*(t)\) to stabilize larger classes of uncertain linear systems.
Reviewer: J.Gayek

MSC:
93D15 Stabilization of systems by feedback
15A24 Matrix equations and identities
93C05 Linear systems in control theory
34D20 Stability of solutions to ordinary differential equations
65K10 Numerical optimization and variational techniques
93B40 Computational methods in systems theory (MSC2010)
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
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