This note deals with the problem of global asymptotic stabilization of linear systems by bounded static feedbacks subject to time delay. Under standard necessary conditions, we provide two constructions of controllers of nested saturation type which extends to the general case partial results of previous papers for arbitrary small bound on the control and large (constant) delay. To validate the approach, a third-order integrator and oscillator with multiplicity two example is presented

Linear Systems Subject to Input Saturation and Time Delay: Global Asymptotic Stabilization

A set of switching sequences of a discrete-time switched linear system is said to be uniformly stabilizing if the system is uniformly exponentially stable over all switching sequences that belong to the set. Based on the recent result that a switched linear system is uniformly stable if and only if an increasing countable union of linear matrix inequality conditions is satisfied, we characterize all uniformly stabilizing sets of switching sequences. A discrete-time hybrid automaton of the automobile engine is considered to illustrate the result

Uniformly Stabilizing Sets of Switching Sequences for Switched Linear Systems

A Gel’fand-type spectral radius formula and stability of linear constrained switching systems☆

The set of stable switching sequences for discrete-time linear switched systems☆

On the complexity and dynamical properties of mixed logical dynamical systems via an automaton-based realization of discrete-time hybrid automaton

The problem of stabilizing linear discrete-time hybrid automata is considered. A synthesis methodology is obtained by extending to hybrid systems the stabilization techniques based on stable convex combinations, originally developed for switching systems. The key idea is exploiting the underlying automaton structure by restricting the control actions to the ones corresponding to cycles in the automaton, which are identified using regular language tools. The so obtained system is equivalent to a regular switching system on which classical stabilization techniques can be applied. An algorithm to explore the candidate stabilizing controller actions is proposed and an application to an automotive engine control problem is described.

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A.L. Sangiovanni-Vicentelli

Papers

On the stabilization of linear discrete-time hybrid automata