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Assuming that the Jacobian has bounded inverse in a neighborhood of the solution (which can indeed be verified for a concrete circuit), by differentiating (9) the circuit equations can be transformed into a non-linear ODE on a manifold as in (5-6) with state variables As mentioned earlier, to reduce the complexity of reachability computation, we will use the hybridization idea. First, the non-linear characteristics in equation (11) can be approximated by a piecewise-affine function of the form: Therefore, the original system is approximated by a hybrid automaton with 3 discrete states (modes).

Stability of computational methods for constrained dynamics systems. SIAM Journal on Scientific Computing 14:95–120, 1993. 8. A. Bemporad and M. Morari. Control of systems integrating logic, dynamics, and constraints, Automatica 35:407-427, 1999. 9. E. L. R. Petzold. Numerical Solution of Initial Value Problems in Ordinary Differential-Algebraic Equations. North Holland, 1989. 10. A. H. Krogh. Verification of polyhedral invariant hybrid automata using polygonal flow pipe approximations. In Hybrid Systems: Computation and Control, LNCS 1569, 76-90, Springer, 1999.

Wallace: A suggestion for a fast multiplier, IEEE Trans. on Computers, EC-13, 2, Feb. 1964. fr Abstract. In this paper we demonstrate a potential extension of formal verification methodology in order to deal with time-domain properties of analog and mixed-signal circuits whose dynamic behavior is described by differential algebraic equations. To model and analyze such circuits under all possible input signals and all values of parameters, we build upon two techniques developed in the context of hybrid (discrete-continuous) control systems.

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