Sets For Discrete-time Linear Systems Research Articles

The Chain Control Set of Discrete-Time Linear Systems on the Affine Two-Dimensional Lie Group

The Chain Control Set of Discrete-Time Linear Systems on the Affine Two-Dimensional Lie Group

Computation of Low Complexity Invariant Sets for Time-Delay Systems: an Optimization-Based Approach

In this paper we propose an optimization approach to compute low-complexity polyhedral invariant sets for discrete-time linear systems affected by delay, based on structural properties related to set factorization. A similarity transformation is conceived as a design tool to bring the dynamic matrix of an augmented representation of the delay difference equation to a block companion form for which low dimensional polyhedral invariant sets with fixed complexity can be found. An optimization problem is formulated to simultaneously compute the similarity transformation and the invariant polyhedron of pre-defined complexity. Numerical experiments illustrate the efficiency of the proposed approach.

On positively invariant sets for discrete-time linear systems with disturbance: an application of maximal disturbance sets

This note concerns the investigation of maximal sets, with respect to which a set is positively invariant, and, given a set a, some properties of /spl Delta/-p.i. sets are analyzed. The approach uses one step of the backward recursion introduced in d'Alessandro and De Santis (1991), where feasibility and optimality conditions for linear dynamical input and/or state constrained systems were analyzed. In Section II, the author gives the main definitions and some basic results. In the subsequent Section III some properties of /spl Delta/-p.i. sets are investigated. The particular case of polyhedral sets is analyzed in Section IV. In Section V, the author shows an application to linear systems with parametric uncertainties in the dynamic matrix A. The author develops a technique to determine a set in the parameters space such that, for any value of the parameter in the set, a given set in the state space is positively invariant. In the last section a numerical example is developed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>