Orthogonal implementations of state variable models

The problem of implementing a specified state variable model using orthogonal computations is addressed. Three approaches, namely, realization embedding, inner product, and matrix factorization are proposed. Output roundoff error and magnitude perturbances are also studied via simulations. The results presented show that orthogonality of the computation can be achieved while simultaneously specifying the dynamical behavior of a system. The advantages of implementing optimal state variable structures, where the optimality is defined in the sense of time-averaged properties, with orthogonal computations which are optimal in terms of numerical conditioning remains an open issue.< >