Related papers: Minimal Realization Problems for Jump Linear Syste…
We here characterize the minimality of realization of arbitrary linear time-invariant dynamical systems through (i) intersection of the spectra of the realization matrix and of the corresponding state submatrix and (ii) moving the poles by…
In this paper, we present a complete stochastic realization theory for stochastic jump-linear systems. We present necessary and sufficient conditions for the existence of a realization, along with a characterization of minimality in terms…
The paper presents realization theory of discrete-time linear switched systems. A discrete-time linear switched system is a hybrid system, such that the continuous sub-system associated with each discrete state is linear. In this paper we…
Finding a positive state-space realization with the minimum dimension for a given transfer function is an open problem in control theory. In this paper, we focus on positive realizations in Markov form and propose a linear programming…
In this paper, we address a collection of state space reachability problems, for linear time-invariant systems, using a minimal number of actuators. In particular, we design a zero-one diagonal input matrix B, with a minimal number of…
In this paper, we study the stabilization of two interdependent Markov jump linear systems (MJLSs) with partial information, where the interdependency arises as the transition of the mode of one system depends on the states of the other…
Differentiable systems in this paper means systems of equations that are described by differentiable real functions in real matrix variables. This paper proposes algorithms for finding minimal rank solutions to such systems over (arbitrary…
This contribution revisits the classical approximate realization problem, which involves determining matrices of a state-space model based on estimates of a truncated series of Markov parameters. A Hankel matrix built up by these Markov…
We consider the entanglement marginal problem, which consists of deciding whether a number of reduced density matrices are compatible with an overall separable quantum state. To tackle this problem, we propose hierarchies of semidefinite…
In this paper, we study the problem of optimizing the stability of positive semi-Markov jump linear systems. We specifically consider the problem of tuning the coefficients of the system matrices for maximizing the exponential decay rate of…
In this paper we consider the low-rank matrix completion problem with specific application to forecasting in time series analysis. Briefly, the low-rank matrix completion problem is the problem of imputing missing values of a matrix under a…
In this paper, we address two minimal controllability problems, where the goal is to determine a minimal subset of state variables in a linear time-invariant system to be actuated to ensure controllability under additional constraints.…
We study a finite-horizon covariance steering problem for discrete-time Markov jump linear systems (MJLS) with both state- and control-dependent multiplicative noise. The objective is to minimize a quadratic running cost while steering the…
The minimum-time control problem consists in finding a control policy that will drive a given dynamic system from a given initial state to a given target state (or a set of states) as quickly as possible. This is a well-known challenging…
A discrete-time linear dynamical system (LDS) is given by an update matrix $M \in \mathbb{R}^{d\times d}$, and has the trajectories $\langle s, Ms, M^2s, \ldots \rangle$ for $s \in \mathbb{R}^d$. Reachability-type decision problems of…
This paper addresses the problem of low-rank distance matrix completion. This problem amounts to recover the missing entries of a distance matrix when the dimension of the data embedding space is possibly unknown but small compared to the…
Switched systems are capable of modeling processes with underlying dynamics that may change abruptly over time. To achieve accurate modeling in practice, one may need a large number of modes, but this may in turn increase the model…
Automated synthesis of provably correct controllers for cyber-physical systems is crucial for deployment in safety-critical scenarios. However, hybrid features and stochastic or unknown behaviours make this problem challenging. We propose a…
Subspace segmentation or subspace learning is a challenging and complicated task in machine learning. This paper builds a primary frame and solid theoretical bases for the minimal subspace segmentation (MSS) of finite samples. Existence and…
Network reconstruction, i.e., obtaining network structure from data, is a central theme in systems biology, economics and engineering. In some previous work, we introduced dynamical structure functions as a tool for posing and solving the…