State deadbeat response and observability in multi-modal systems

Sampling and control of switched linear systems

“…A constructive procedure was provided in [12] to calculate the desired feedback gain matrices and the switching index sequence for third-order discrete-time switched systems. Based on this procedure, we propose an algorithm to compute a stabilizing switching path and corresponding gain matrices.…”

“…That is, any two states in the controllable subspace of the original (continuous-time) system can be driven to each other via appropriate synchronous switching and (piecewise constant) digital control. One contribution of this result lies in the fact that there has already been done a lot of work for discretetime switched linear systems [10][11][12]. Due to the above connection, the tools for discrete-time systems can be utilized to investigate continuous-time systems and the existing results can be converted into parallel results for the continuous-time counterpart.…”

Sampling and control of switched linear systems

“…The feedback stabilization problem of the discrete-time system has been addressed in [3]. The following lemma is for third-order systems.…”

“…Constructive procedures were also provided in [3] to calculate the desired feedback matrices and the switching index sequence. R e m a r k 5 By the above results, the closed-loop system will conuerge within four periods of sampling.…”

On observability and reachability in a class of discrete-time switched linear systems

“…The problem of determining the existence of a reachable path for (2) has eluded researchers for a long time, and, to the best of our knowledge, the only efforts in studying the existence of reachable paths for (2) can be found in [2], [3], [4], [5], [6]. First, in a series of papers [2], [3], [6], Stanford and Conner studied the structure of the reachable set of switched linear systems, and showed that it was a subspace of R n in reversible (i.e., with invertible A(θ k ) matrices) systems [6], and, in general, a union of arbitrarily many maximal subspaces in [3].…”