Existence and uniqueness of solutions of linear variable coefficient discrete-time descriptor 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...

Eigenvalue Assignment Of Discrete-Time Linear Systems With State And Input Time-Delays

Time-delays are important components of many dynamical systems that describe coupling or interconnection between dynamics, propagation or transport phenomena, and heredity and competition in population dynamics. The stabilization with time delay in observation or control represents difficult mathematical challenges in the control of distributed parameter systems. It is well-known that the stabi...

Explicit solutions of regular linear discrete-time descriptor systems with constant coefficients

Explicit solution formulas are presented for systems of the form Exk+1 = Axk + fk with k ∈ K, where K ⊂ Z is a discrete interval and the pencil λE − A is regular. Different results are obtained when one starts with an initial condition at the point k = 0 and calculates into the future (i.e., Exk+1 = Axk + fk with k ∈ N) and when one wants to get a complete solution (i.e., Exk+1 = Axk + fk with ...

Existence and uniqueness of unmixed solutions of the discrete-time algebraic Riccati equation

A solution X of a discrete-time algebraic Riccati equation is called unmixed if the corresponding closed-loop matrix Φ(X) has the property that the common roots of det (sI−Φ(X)) and det (I− sΦ(X)∗) (if any) are on the unit circle. A necessary and sufficient condition is given for existence and uniqueness of an unmixed solution such that the eigenvalues of Φ(X) lie in a prescribed subset of C. A...

Existence , Uniqueness , and Extendibility of Solutions of Volterra Integral Systems with Multiple , Variable Lags