Journal ArticleDOI
Perspectives and results on the stability and stabilizability of hybrid systems
R.A. Decarlo,Michael S. Branicky,Stefan Pettersson,Bengt Lennartson +3 more
- Vol. 88, Iss: 7, pp 1069-1082
TLDR
In this paper, the authors introduce the concept of hybrid systems and some of the challenges associated with the stability of such systems, including the issues of guaranteeing stability of switched stable systems and finding conditions for the existence of switched controllers for stabilizing switched unstable systems.Abstract:
This paper introduces the concept of a hybrid system and some of the challenges associated with the stability of such systems, including the issues of guaranteeing stability of switched stable systems and finding conditions for the existence of switched controllers for stabilizing switched unstable systems. In this endeavour, this paper surveys the major results in the (Lyapunov) stability of finite-dimensional hybrid systems and then discusses the stronger, more specialized results of switched linear (stable and unstable) systems. A section detailing how some of the results can be formulated as linear matrix inequalities is given. Stability analyses on the regulation of the angle of attack of an aircraft and on the PI control of a vehicle with an automatic transmission are given. Other examples are included to illustrate various results in this paper.read more
Citations
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Journal ArticleDOI
Robust uniformly ultimate boundedness control for uncertain switched linear systems
TL;DR: Under arbitrary switching laws, a continuous state feedback control scheme is proposed in order to guarantee uniformly ultimate boundedness of every system response within an arbitrary small neighborhood of the zero state.
Journal ArticleDOI
A common functional observer scheme for three systems with unknown inputs
TL;DR: The existence conditions of the scheme allow the observers to be designed independently of each other which greatly simplify the design process, and also serve as a basis of comparison for future development of common functional observer schemes.
Journal ArticleDOI
Event‐triggered state‐dependent switching rule design for switched linear systems
Journal ArticleDOI
Stability analysis of switched systems with general nonlinear disturbances
TL;DR: By using generalized Gronwall–Bellman inequalities, stability results for the systems with arbitrary switching laws are obtained and an example is given to illustrate the effectiveness of the results obtained.
Journal ArticleDOI
Hybrid control synthesis for eventuality specifications using level set methods
A. Trontis,M.P. Spathopoulos +1 more
TL;DR: In this article, the authors proposed a dynamic programming algorithm that computes the maximal initial set and a controller with the desired property, where the boundary of the reachable set is characterized as the zero level set of a Hamilton-Jacobi equation.
References
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Book
Applied Nonlinear Control
TL;DR: Covers in a progressive fashion a number of analysis tools and design techniques directly applicable to nonlinear control problems in high performance systems (in aerospace, robotics and automotive areas).
Book
Linear Matrix Inequalities in System and Control Theory
TL;DR: In this paper, the authors present a brief history of LMIs in control theory and discuss some of the standard problems involved in LMIs, such as linear matrix inequalities, linear differential inequalities, and matrix problems with analytic solutions.
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Differential Equations with Discontinuous Righthand Sides
TL;DR: The kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics, algebraic geometry interacts with physics, and such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes.