This paper studies the stochastic cooperative output regulation problem for linear discrete-time multi-agent systems (MASs) with Markov switching topologies and communication/input delays. First, a moment stability criterion for an interconnected time-homogeneous Markov jump linear systems is builded. Then, based on the moment stability criterion, a fully distributed output regulation protocol is designed to solve the stochastic cooperative output regulation problem successively. Finally, a numerical simulation is provided to validate the efficiency of the designed protocol.

This paper studies the differential flatness of time-delay systems (TDSs). Based on factorizations in the pseudo-polynomials ring, a flat output for the single-input linear commensurate TDS (namely, the delays in the system are multiplies of a certain unit delay) is constructed explicitly. Then the TDS can be converted into a high-order fully actuated system (HOFAS) model with the generalized state as the flat output, and the finite spectrum assignment (FSA) problem can be solved immediately by using the HOFAS approach, which provides some new insight into the study of the FSA problem. By parameterizing the considered TDS via the constructed flat output and applying the interpolation theory, the state trajectory planning problem and state tracking problem are solved, resulting a two-degree-of-freedom (2DOF) controller. Numerical examples demonstrates the effectiveness of the presented approach.

Stability analysis is considered in this paper for linear neutral delay systems subject to two different delays in both the state variables and the retarded derivatives of state variables. By choosing a suitable state vector indexed by an integer$k$, a new augmented Lyapunov-Krasovskii functional (LKF) is constructed, and a stability criterion based on linear matrix inequalities is developed accordingly. It is shown that the proposed condition is less conservative than the existing methods due to the introduction of the delay-product-type integral terms in the LKF. The resulting stability criterion is then applied to the robust stability analysis of neutral delay systems with norm-bounded uncertainty. Moreover, a delay-independent stability criterion is developed based on the proposed LKF, and its frequency-domain interpretation is also given. These developed stability criteria indexed by an integer$k$exhibit a hierarchical character: the larger the integer$k$, the less conservatism of the resulting stability criterion. Finally, two numerical examples are carried out to illustrate the effectiveness of the proposed method.