Proceedings ArticleDOI
On the stabilization of linear discrete-time hybrid automata
M. Zoncu,A. Balluchi,A.L. Sangiovanni-Vicentelli,A. Bicchi +3 more
- Vol. 2, pp 1147-1152
TLDR
A synthesis methodology is obtained by extending to hybrid systems the stabilization techniques based on stable convex combinations, originally developed for switching systems, which is equivalent to a regular switching system on which classical stabilization techniques can be applied.Abstract:
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.read more
Citations
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Journal ArticleDOI
Linear Systems Subject to Input Saturation and Time Delay: Global Asymptotic Stabilization
Karim Yakoubi,Yacine Chitour +1 more
TL;DR: Under standard necessary conditions, two constructions of controllers of nested saturation type are provided which extends to the general case partial results of previous papers for arbitrary small bound on the control and large (constant) delay.
Journal ArticleDOI
Uniformly Stabilizing Sets of Switching Sequences for Switched Linear Systems
Ji-Woong Lee,Geir E. Dullerud +1 more
TL;DR: 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.
Journal ArticleDOI
A Gel’fand-type spectral radius formula and stability of linear constrained switching systems☆
TL;DR: This paper presents a Gel'fand-type spectral radius formula which states that the joint spectral radius is equal to the generalized spectral radius for a matrix multiplicative semigroup restricted to a subset that need not carry the algebraic structure of $\bS^+$.
Journal ArticleDOI
The set of stable switching sequences for discrete-time linear switched systems☆
TL;DR: In this paper, a lower bound of the Hausdorff dimension of the set of asymptotically stable switching sequences is derived for discrete-time switched linear systems.
References
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Journal ArticleDOI
Multiple Lyapunov functions and other analysis tools for switched and hybrid systems
TL;DR: Bendixson's theorem is extended to the case of Lipschitz continuous vector fields, allowing limit cycle analysis of a class of "continuous switched" systems.
Journal ArticleDOI
Control of systems integrating logic, dynamics, and constraints
Alberto Bemporad,Manfred Morari +1 more
TL;DR: A predictive control scheme is proposed which is able to stabilize MLD systems on desired reference trajectories while fulfilling operating constraints, and possibly take into account previous qualitative knowledge in the form of heuristic rules.
Journal ArticleDOI
Supervisory control of families of linear set-point controllers - Part I. Exact matching
TL;DR: It is shown that in the absence of unmodeled process dynamics, the proposed supervisor can successfully perform its function even if process disturbances are present, provided they are bounded and constant.
Journal ArticleDOI
Computation of piecewise quadratic Lyapunov functions for hybrid systems
Mikael Johansson,Anders Rantzer +1 more
TL;DR: The search for a piecewise quadratic Lyapunov function is formulated as a convex optimization problem in terms of linear matrix inequalities and the relation to frequency domain methods such as the circle and Popov criteria is explained.