Worst-case tolerance analysis of linear DC and AC electric circuits

This paper addresses the problem of worst-case tolerance analysis of steady states in linear DC and AC electric circuits. The statement of the problem considered is in the form of linear algebraic equations whose elements are, in the general case, nonlinear functions of a given set of independent interval parameters. Three kinds of solutions are considered: 1) outer solution; 2) inner solution and 3) exact solution. A direct method for computing an outer solution and an iterative method for finding an inner solution are suggested. The inner and outer solutions thus found provide a tight two-sided bound on the exact solution of the tolerance problem investigated. The exact solution can be determined if certain monotonicity conditions are fulfilled. The verification of the conditions involves solving several associated outer solution problems. The computational efficiency of the methods suggested is demonstrated by a numerical example.