Algebraic Solution of Riccati Equations in Discrete, Periodically Time-Varying System with Detectability and Stabilizability

Stabilizability and detectability of discrete-time time- varying systems

In this paper we introduce some notions of stabilizability and detectability for discrete time-varying systems. These concepts are introduced by making state-space decompositions of the system. This allows an intuitive interpretation and shows the difficulties which occur if one tries to derive general stabilizability and detectability properties. Moreover, we show by means of a counterexample ...

Discrete Time H∞ Algebraic Riccati Equations

Transformations Between Discrete-time and Continuous-time Algebraic Riccati Equations

We introduce a transformation between the discrete-time and continuoustime algebraic Riccati equations. We show that under mild conditions the two algebraic Riccati equations can be transformed from one to another, and both algebraic Riccati equations share common Hermitian solutions. The transformation also sets up the relations about the properties, commonly in system and control setting, tha...

Temporal and One-Step Stabilizability and Detectability of Time-Varying Discrete-Time Linear Systems

Time-varying discrete-time linear systems may be temporarily uncontrollable and unreconstructable. This is vital knowledge to both control engineers and system scientists. Describing and detecting the temporal loss of controllability and reconstructability requires considering discrete-time systems with variable dimensions and the j-step, k-step Kalman decomposition. In this note for linear dis...

Large-Scale Discrete-Time Algebraic Riccati Equations — Numerically Low-Ranked Solution, SDA and Error Analysis∗

We consider the solution of large-scale discrete-time algebraic Riccati equations with numerically low-ranked solutions. The structure-preserving doubling algorithm (SDA) will be adapted, with the iterates for A not explicitly computed but in the recursive form Ak = Ak−1−D (1) k Sk[D (2) k ] >, where D (1) k and D (2) k are low-ranked with Sk being small in dimension. With n being the dimension...