## A Mathematical Theory for the Analysis of a Class of Nonlinear Systems |

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analytic Appendix applied arise assumed auxiliary equation auxiliary function behavior boundary conditions boundary values bounded calculated canonical chapter circuit conditions specified consider constant continuous function convex set convex singularity hull corresponding defined determine domain driving function entire function evident example exists exponential type finite forcing function fron function of exponential function x(t given half plane Hence impulsive response indicator function infinity initial conditions initial point input Integral k-th Laplace transform linear system linear terns Lipschitz condition modified multiplication n-th nonlinear differential equation nonlinear functions nonlinear system obtained operator physical systems Picard Iter polynomial possible power series previously properties radius of convergence recurrence relation recursion formula restrictions riven s-plane series solution shown singular point Sn(t solving sone Stability Theory Substituting Suppose Taylor series terns tine tion variable xn(t xo(t xQ(t yields zero