H2 preview control in the discrete-time domain is approached in a strict geometric perspective. The original formulation in the frequency domain is recast in the time domain. Then, it is shown how the problem in the time-domain can be reduced to the combination of elementary subproblems. This approach requires a structural analysis of the properties of the singular Hamiltonian system associated...

A descriptor system describes a natural representation for physical systems. In general, the continuous-time descriptor representation consists of differential and algebraic equations, and the discrete-time descriptor system has difference and algebraic equations. Hence, the descriptor system is a generalized representation of the state-space system. This system appears in various physical syst...

We present discrete-time stochastic extremum seeking algorithms and prove their convergence using stochastic averaging theory that we recently developed. First, we provide a discrete stochastic extremum seeking algorithm for a static map, in which measurement noise is considered and an ergodic discrete-time stochastic process is used as the excitation signal. Second, for discrete-time nonlinear...

An LQ optimal tracker will achieve zero tracking error when the input penalty is removed. However, the problem becomes singular, and a solution hides behind several coordination transformations. We will highlight a discrete time version of this singular LQ optimization. We will also present data-based formulas to design this optimal tracker at the absence of a parametric plant model. We will sh...

In this paper, the moving horizon recursive state estimator for linear singular systems is derived from the least squares estimation problem. It will be shown that this procedure yields the same state estimate as the Kalman filter for descriptor systems when the noises are Gaussian. The obtained results are applied to the state and the unknown inputs estimation for discrete-time systems with un...

In this paper, necessary and sufficient conditions for the positive invariance of convex polyhedra with respect to linear discrete-time singular systems subject to bounded additive disturbances are established. New notions of ∆-invariance under different assumptions on the initial conditions are defined. Specifically, the notions of simple and weak ∆invariance are considered. They can be seen a...

In this article we focus our attention on the relation between consistent and non-consistent initial conditions of a class of singular linear discrete time systems. First we analyze how both types of initial conditions are connected to the column vector space of the finite and the infinite eigenvalues of the related to the singular system matrix pencil and after we prove that a non-consistent i...

A method for solving the descriptor discrete-time linear system is focused. For easily, it is converted to a standard discrete-time linear system by the definition of a derivative state feedback. Then partial eigenvalue assignment is used for obtaining state feedback and solving the standard system. In partial eigenvalue assignment, just a part of the open loop spectrum of the standard linear s...

-In this paper, we propose a simple approach to analyse stability robustness of discrete-time singular systems under structured perturbations. The developed robustness criteria are then applied to solve robust regional poleassignment problems of singular systems. A robust control design algorithm, via state feedback, is also given. The robust stability problem of singular systems is more compli...

The paper is concerned with the hidden dynamic state estimation in linear discrete-time stochastic systems in presence of Gaussian noises. The associated with the state-space model estimator is known as the Kalman filter (KF). One of the shortcomings of this recursive algorithm is its numerical instability with respect to roundoff errors. Since the appearance of the KF in 1960s, much effort has...