Observer design for a class of nonlinear systems combining dissipativity with interconnection and damping assignment

A nonlinear observer design approach is proposed that exploits and combines port-Hamiltonian systems and dissipativity theory. First, a passivity-based observer design using interconnection and damping assignment for time variant state affine systems is presented by applying output injection to the system such that the observer error dynamics takes a port-Hamiltonian structure. The stability of the observer error system is assured by exploiting its passivity properties. Second, this setup is extended to develop an observer design approach for a class of systems with a time varying state affine forward and a nonlinear feedback contribution. For a class of nonlinear systems, the theory of dissipative observers is adapted and combined with the results for the passivity-based observer design using interconnection and damping assignment. The convergence of the compound observer design is determined by a linear matrix inequality. The performance of both observer approaches is analyzed in simulation examples

Global entrainment of transcriptional systems to periodic inputs

This paper addresses the problem of giving conditions for transcriptional systems to be globally entrained to external periodic inputs. By using contraction theory, a powerful tool from dynamical systems theory, it is shown that certain systems driven by external periodic signals have the property that all solutions converge to a fixed limit cycle. General results are proved, and the properties are verified in the specific case of some models of transcriptional systems. The basic mathematical results needed from contraction theory are proved in the paper, making it self-contained