Qualitative Theory of Hybrid Dynamical SystemsHybrid dynamical systems, both continuous and discrete dynamics and variables, have attracted considerable interest recently. This emerging area is found at the interface of control theory and computer engineering, focusing on the analogue and digital aspects of systems and devices. They are essential for advances in modern digital- controller technology. "Qualitative Theory of Hybrid Dynamical Systems" provides a thorough development and systematic presentation of the foundations and framework for hybrid dynamical systems. The presentation offers an accessible, but precise, development of the mathematical models, conditions for existence of limit cycles, and criteria of their stability. The book largely concentrates on the case of discretely controlled continuous-time systems and their relevance for modeling aspects of flexible manufacturing systems and dynamically routed queuing networks. Features and topics: *differential automata*development and use of the concept "cyclic linear differential automata" (CLDA)*switched single-server flow networks coverage*application to specific models of manufacturing systems and queuing networks*select collection of open problems for the subject*self-contained presentation of topics, with the necessary background This new book is an excellent resource for the study and analysis of hybrid dynamical systems used in systems and control engineering. Researchers, postgraduates and professionals in control engineering and computer engineering will find the book an up-to-date development of the relevant new concepts and tools. |
Contents
Qualitative Analysis of Some Simple Hybrid | 13 |
General Theory of Multivalued Differential Automata | 43 |
TwoDimensional Hybrid Dynamical Systems | 105 |
Limit Cycles in Hybrid Dynamical Systems with | 219 |
Globally Periodic Behavior of Switched Single Server | 305 |
Other editions - View all
Qualitative Theory of Hybrid Dynamical Systems Alexey S. Matveev,Andrey V. Savkin Limited preview - 2012 |
Qualitative Theory of Hybrid Dynamical Systems Alexey S. Matveev,Andrey V. Savkin No preview available - 2012 |
Qualitative Theory of Hybrid Dynamical Systems Alexey S. Matveev,Andrey V. Savkin No preview available - 2000 |
Common terms and phrases
analysis assume Assumption automata bounded buffer called chapter closed completes component condition connected Consider consists constant contains continuous control policy converges correspondence cyclic defined Definition Denote described differential automaton discrete edge elements empty equals equation event example exhibits exists exit face FIGURE finite number flow network function Furthermore given gives graph hold hybrid systems implies initial intersection interval introduced invariant domain Lemma limit cycle lying means Moreover multivalued nodes Note obtained passing path periodic trajectory positive problem Proof prove range recall region relation remains Remark respectively runs satisfies segment sequence shown simple solution stability starting statement Suppose switched server system switching points switching policy symbolic taking Theorem tion topological true unique values vector violation yields