Theory and computation of disturbance invariant sets for discrete-time linear systems

Optimal Finite-time Control of Positive Linear Discrete-time Systems

This paper considers solving optimization problem for linear discrete time systems such that closed-loop discrete-time system is positive (i.e., all of its state variables have non-negative values) and also finite-time stable. For this purpose, by considering a quadratic cost function, an optimal controller is designed such that in addition to minimizing the cost function, the positivity proper...

Linear Time-Invariant Systems with Discrete Time

Invariant Approximations and Disturbance Attenuation for Constrained Linear Discrete-Time Systems

This paper presents a new method to the invariant approximations and disturbance attenuation for constrained Linear Discrete-Time Systems. A novel condition in the form of LMIs is derived to guarantee the asymptotically stable of the system, based on which an optimization problem is constructed to compute the approximation of an invariant set contained in the domain of attraction. This new meth...

Passive linear discrete time-invariant systems

We begin by discussing linear discrete time-invariant i/s/o (input/state/output) systems that satisfy certain ‘energy’ inequalities. These inequalities involve a quadratic storage function in the state space induced by a positive self-adjoint operator H that may be unbounded and have an unbounded inverse, and also a quadratic supply rate in the combined i/o (input/output) space. The three most ...

Invariant Sets for a Class of Discrete-time Lur’e Systems

We present a method to estimate the domain of attraction of a class of discretetime Lur’e systems. A new notion of LNL-invariance, stronger than the traditional invariance concept, is introduced. An algorithm to determinate the largest LNL-invariant set for this class of systems is proposed. Moreover, it is proven that the LNL-invariant sets provided by this algorithm are polyhedral convex sets...