This paper is devoted to data-driven control methods for discrete linear time-invariant systems based on controller design from finite sets of input-output measurements of a system with unknown matrices. The discussed approach is also characterized by the use of linear matrix inequalities. We consider methods based on the Fundamental Lemma and the concept of Data Informativity for quadratic stabilization of a system (with exact data and in the case of bounded exogenous disturbances affecting the system), optimal linear quadratic regulator design, and H2- and H∞-optimal control design. The application features of the methods are considered; their advantages and disadvantages are discussed; and numerical examples are provided to illustrate their performance.

The paper addresses the problem of robust and safe implementation of a state predictor used for stabilization of the linear time-invariant system with known arbitrarily large yet bounded input delay. To this end, we design a new simple observer with resetting of initial conditions generating an estimate of the state prediction error. This estimate is used as the feedback for closed-loop correction of the state prediction. The robustness of the proposed closed-loop predictor with respect to parametric perturbations as well as to its numerical realization is proved and illustrated by simulation.

In the paper, we propose algorithms for solving terminal stabilization and timeoptimization problems for discrete-time linear dynamical systems with convex sets of geometric constraints on the control. The algorithms are based on the well-known block coordinate descent method. We present some corollaries to classical results and give new assertions on the convergence of the constructed algorithms to a solution in the problems.

This paper considers systems of nonlinear ordinary differential equations with a continuous right-hand side. For such systems, stability analysis of the trivial equilibrium with respect to part of the variables is performed in the context of the direct Lyapunov method. Lyapunov functions are constructed by choosing an appropriate pair of a main Lyapunov function and an auxiliary function: the latter function is used to correct the domain of the state space of the system where the former function is introduced and analyzed. Illustrative examples are provided in which such pairs are constructed for some nonlinear systems of two and three differential equations.

It is shown that three variants of the optimal iterative learning problem — maximizing the expected result for a fixed total number of trials and time; minimizing the time to achieve a given expected result; minimizing the number of trials required to achieve a given expected result — have either a degenerate (independent of the learning intensity dynamics) or a trivial (maximum permissible learning intensity) solution.