Class Of Discrete-time Hybrid Systems Research Articles

On Asymptotic Stability of Discrete-Time Hybrid Systems

In this brief, we consider the asymptotic stability problem of a novel class of discrete-time hybrid systems. First, we introduce the so-called system in detail, which consists of discrete-time continuous-valued and Boolean dynamics. Second, we give the algebraic form of the systems by using the Khatri-Rao product and semi-tensor product (i.e., Cheng product). Third, we propose the concept of asymptotic stability for the hybrid systems. Further, based on Lyapunov functions, a necessary and sufficient condition is derived for testing asymptotic stability. Finally, a numerical example is presented to illustrate the effectiveness of the theoretical results.

A New Robust Nonfragile Controller Design Scheme for a Class of Hybrid Systems through Piecewise Affine Models

This paper investigates the robust H∞ nonfragile control problem for a class of discrete-time hybrid systems based on piecewise affine models. The objective is to develop an admissible piecewise affine nonfragile controller such that the resulting closed-loop system is asymptotically stable with robust H∞ performance γ. By employing a state-control augmentation methodology, some new sufficient conditions for the controller synthesis are formulated based on piecewise Lyapunov functions (PLFs). The controller gains can be obtained via solving a set of linear matrix inequalities. Simulation examples are finally presented to demonstrate the feasibility and effectiveness of the proposed approaches.

Asymptotically optimal controls of hybrid linear quadratic regulators in discrete time

This work develops asymptotically optimal controls for a class of discrete-time hybrid systems involving singularly perturbed Markov chains having weak and strong interactions. The state space of the underlying Markov chain is decomposed into a number of recurrent classes and a group of transient states. Using a hierarchical control approach, by aggregating the states in each recurrent class into a single state, a continuous-time quadratic limit control problem in which the resulting limit Markov chain has much smaller state space is derived. Using the optimal control for the limit problem, a control for the original problem is constructed, which is shown to be nearly optimal. Finally, a numerical example is given to demonstrate the effectiveness of the approximation scheme.