No abstract

No abstract

We define the dual truncated Toeplitz operators and give some basic properties of them. In particular, spectrum and reducing subspaces of some special dual truncated Toeplitz operator are characterized.

This paper deals with the simultaneous stabilization problem for a family of discrete time‐varying linear systems in the framework of nest algebra. Under the transmission condition, a necessary and sufficient condition for simultaneous "stabilizability" is established in terms of single strong representation for only one controller in the transmission condition, in which the resulting characterization involves no strong representation of the plants compared to previous work.

This paper studies the asymptotic behavior of infinite dimensional systems determined by polynomial shift operators. The results from ergodic theory and C0‐semigroups are used to obtain a characterization of those initial states which lead to convergent solutions. Estimates on the rate of convergence for solutions are obtained under a stronger ergodic condition on corresponding initial states. The results can be used to solve the robot rendezvous problem and investigate platoon systems.

This paper considers robust output consensus of discrete-time networked homogeneous negative imaginary (NI) systems under 𝓁 2 external disturbances via integral quadratic constraints (IQCs). A necessary and sufficient condition for robust output consensus of discrete-time networked NI systems without poles at ±1 is obtained by the IQC-based discrete-time NI (D-NI) stability result.Moreover, the robust output consensus problem can be solved by designing an unstable controller whose poles are related to transmission zeros of D-NI systems. The case of discrete-time networked NI systems with poles at 1 is also studied. These main results are related to all eigenvalues of the Laplacian matrix of the network graph as well as the corresponding complementary IQCs at ±1 frequencies. Some corollaries are given by constructing appropriate IQC multipliers in order to simplify the main results. Finally, three examples are shown to explain the validity of the main results.

No abstract