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Nonlinear Systems Analysis. , 1993. 23. A. Yakubovich. Solution of certain matrix inequalities in the stability theory of nonlinear control systems (English translation). Soviet. Math. , 3~620-623, 1962. 24. A. K. Gelig. Stability of stationary sets in control systems with discontinuous nonlinearities. World Scientific, 2004. Previously available in Russian under the title “Stability of nonlinear systems with non-unique equilibria”, Nauka, 1978. CHAPTER 2 Nonlinear Control of Feedforward Systems G.

16) and suppose { A ,B } is controllable, F E R n x nis a Hurwitz matrix and J E R P x P is such that (A2) holds. 20) and A,l = A - BKC is Hurwitz. 20) rewrites > 0 to be selected. 22) 1' < 0. 22) holds. 24) = 0, for all H , F, J and all positive constants x. 22) reduces to [ x(J + J ' ) 0 0 T + PcF + F'Pc + PcGG'Pc where T Since + + + Y ' H H'Y Y'RR'Y + Y'RG'Pc + PcGR'Y = Y'(H RG'Pc) (HI + PcGR')Y + Y'RR'Y. , T + PcF + F'Pc + PcGG'Pc 5 0. 25) = -(GG'+I). Then, < 0. 26) Hence, it is sufficient to show that T can be made arbitrarily small.

2' .... ; . . . . . . . . . . . . . 5. 78). time, the new stabilization scheme provides motivation for a dynamic outp u t feedback stabilization methodology, which can accommodate saturated outputs. This dynamic solution is clearly different from observation-based schemes available in t h e literature. Bibliography 1. M. R. V. Kokotovik. Robust nonlinear control of feedforward systems with unmodeled dynamics. Automatica, 37:265-272, 2001. 2. A. Astolfi, R.