Quantized Feedback Stabilization of Sampled-Data Switched Linear Systems

We propose a stability analysis method for sampled-data switched linear systems with quantization. The available information to the controller is limited: the quantized state and switching signal at each sampling time. Switching between sampling times can produce the mismatch of the modes between the plant and the controller. Moreover, the coarseness of quantization makes the trajectory wander around, not approach, the origin. Hence the trajectory may leave the desired neighborhood if the mismatch leads to instability of the closed-loop system. For the stability of the switched systems, we develop a sufficient condition characterized by the total mismatch time. The relationship between the mismatch time and the dwell time of the switching signal is also discussed.Comment: 17 pages, 3 figure

Stability is realization-dependent: some examples

This paper gives some examples with the same impulse response, both approximately controllable and observable, but one of them is exponentially stable and the other is unstable. Some related spectral properties are also investigated

Signal Reconstruction via H-infinity Sampled-Data Control Theory: Beyond the Shannon Paradigm

This paper presents a new method for signal reconstruction by leveraging sampled-data control theory. We formulate the signal reconstruction problem in terms of an analog performance optimization problem using a stable discrete-time filter. The proposed H-infinity performance criterion naturally takes intersample behavior into account, reflecting the energy distributions of the signal. We present methods for computing optimal solutions which are guaranteed to be stable and causal. Detailed comparisons to alternative methods are provided. We discuss some applications in sound and image reconstruction

Module structure of constant linear systems and its applications to controllability

AbstractWe shall introduce a new module structure to a large class of continuous-time constant linear systems. This is done as a natural extension of the classical k[z]-module structure of finite-dimensional constant linear systems. This module action is used to investigate the relationship between reachability and controllability of linear systems. After introducing the notion of K-controllability due to Kamen [12], we give the following result in Section 5: If a constant linear system is described by a functional differential equation ẋ = Fx + Gu, where x and G belong to a Banach space X, and if G is K-controllable to zero, then every reachable state is reachable and controllable in bounded time. (The result given in Section 5 is a little more general than this.) We also give a simple example in Section 6 to illustrate this result