We describe a recently developed Descriptor Systems Toolbox implemented under Matlab. This Toolbox relies on the object oriented approach for control systems analysis and design provided within the standard Control Toolbox of Matlab. The basic approach to develop the Descriptor Systems Toolbox was to exploit the powerful matrix and system object manipulation features of Matlab via flexible and ...

This paper addresses the problem of constructing controlled invariant polyhedral sets for linear discrete-time descriptor systems subject to state and control constraints and persistent disturbances. Regardless the large number of contributions on set invariance for linear systems in the standard form, there are few works dealing with set invariance properties in the case of descriptor systems....

In this paper necessary and sufficient conditions are derived for complete reachability and observability of periodic time-varying descriptor systems. Applying these conditions, the symmetric positive semi-definite reachability/observability Gramians are defined and can be shown to satisfy some projected generalized discrete-time periodic Lyapunov equations. We propose a numerical method for so...

This paper deals with discrete-time stochastic descriptor (singular) systems with instantaneous and multi-time delayed measurements. The estimability condition of the descriptor systems involving delayed measurements is given. Using the measurements reorganization approach, the optimal Kalman …lter and corresponding estimate error covariance are derived. Furthermore, an algorithm for the linear...

In the sequel to [12], we discuss behavioural approach for linear, time-varying, differential algebraic (descriptor) systems with real analytic coefficients. The analysis is “almost global” in the sense that the analysis is not restricted to an interval I ⊂ R but is allowed for the “time axis” R\T, where T is a discrete set of critical points, at which the solution may exhibit a finite escape t...

For discrete-time descriptor syslems, various generalized Lyapunov equations were studied in the literature. Howevn these well known generalized Lyapunov equations can be used only under some restrictive assumptions on the plant (as system regularity, or positiveness of a Q matrix, for example). To overcome these limitations, we propose in this paper a new generalized Lyapunov equation for disc...

The linear quadratic zero-sum dynamic game for discrete time descriptor systems is considered. A method, which involves solving a linear quadratic zero-sum dynamic game for a reduced-order discrete time state space system, is developed to nd the linear feedback saddle-point solutions of the problem. Checkable conditions, which are described in terms of two dual algebraic Riccati equations and a...

From the necessary and sufficient conditions for complete reachability and observability of periodic time-varying descriptor systems, the symmetric positive semi-definite reachability/observability Gramians are defined. These Gramians can be shown to satisfy some projected generalized discrete-time periodic Lyapunov equations. We propose a numerical method for solving these projected Lyapunov e...

Necessary and sufficient conditions for the positivity and reachability of fractional descriptor positive discrete-time linear systems are established. The minimum energy control problem for the descriptor positive systems with bounded inputs is formulated and solved. Sufficient conditions for the existence of solution to the minimum energy control problem are given. Procedure for computation o...

These are additional figures and tables related to our dataset. The additional file input.csv.gz includes the input data as comma separated matrix, which can be read by most spreadsheet applications or the R code data <read.csv("input.csv", row.names=1). The first row is the atomID as stored in NMRshiftDB, the remaining 246 columns are the descriptor values with at most 50% NA values. The categ...