Ricerc@Sapienza

This letter deals with the geometric characterization of the zero-dynamics for linear time-invariant systems with aperiodic time-driven jumps. As the intuition suggests, it is given by the restriction of the dynamics onto the largest subspace over which the trajectories are constrained to ensure zero output. Such a dynamics is characterized by a subset of the flowing zeros and a subset of the zeros which can be fictitiously associated to the jumping dynamics.

The paper deals with the characterization of a dummy ’output function’ associated with the stable component of the zero-dynamics of a linear square multi-input multi-output system. With reference to the 4-Tank dynamics, it is shown how such a procedure, applied to the linear tangent model of a nonlinear plant, may be profitably applied to assure local stability in closed loop.

We present a solver for a class of sparse linear systems that we call quasi block diagonal. The solver combines multi-processors and multi-threaded parallelisms using MPI and OpenMP to implement preconditioned Jacobi. Specific formats for sparse matrices are exploited in order to reduce memory storage requirements. Our experiments show that communication costs are negligible, so as that speed-up and efficiency with respect to the sequential implementation are very high. Our hybrid implementation is tested on a cluster and compared to Intel MKL PARDISO linear solver.