From the reviews: "This monograph covers a wide range of nonlinear dynamical systems, including Jurdjevic-Quinn systems, time-varying systems satisfying LaSalle or Matrosov conditions, adaptively controlled dynamics, slowly and rapidly time-varying systems, and hybrid time-varying systems. ... The book will be useful to researchers and graduate students in various areas of applied mathematics and control theory and engineering." (Vladimir Sobolev, Zentralblatt MATH, Vol. 1186, 2010) "This is an important and painstaking chore. ... The book is a combination of a research monograph and an expository text. ... those who need to analyze or to perform a detailed stability or stabilization analysis of concrete equations will find the book a very good source of ideas and references. ... should be a desired addition to all libraries that serve mathematics departments and control engineering faculties. ... could be used successfully as reading material for advanced graduate students interested in the subject matter." (Zvi Artstein, SIAM Review, Vol. 53 (1), 2011)

• Background.- Background on Nonlinear Systems.- Review of Lyapunov Functions.- Time-Invariant Case.- Matrosov Conditions: Simple Case.- Jurdjevic-Quinn Conditions.- Systems Satisfying the Conditions of LaSalle.- Time-Varying Case.- Strictification: Basic Results.- Backstepping for Time-Varying Systems.- Matrosov Conditions: General Case.- Adaptively Controlled Systems.- Systems with Multiple Time Scales.- Rapidly Time-Varying Systems.- Slowly Time-Varying Systems.- Hybrid Time-Varying Systems.

From the reviews: "This monograph covers a wide range of nonlinear dynamical systems, including Jurdjevic-Quinn systems, time-varying systems satisfying LaSalle or Matrosov conditions, adaptively controlled dynamics, slowly and rapidly time-varying systems, and hybrid time-varying systems. ... The book will be useful to researchers and graduate students in various areas of applied mathematics and control theory and engineering." (Vladimir Sobolev, Zentralblatt MATH, Vol. 1186, 2010) "This is an important and painstaking chore. ... The book is a combination of a research monograph and an expository text. ... those who need to analyze or to perform a detailed stability or stabilization analysis of concrete equations will find the book a very good source of ideas and references. ... should be a desired addition to all libraries that serve mathematics departments and control engineering faculties. ... could be used successfully as reading material for advanced graduate students interested in the subject matter." (Zvi Artstein, SIAM Review, Vol. 53 (1), 2011)

• Background.- Background on Nonlinear Systems.- Review of Lyapunov Functions.- Time-Invariant Case.- Matrosov Conditions: Simple Case.- Jurdjevic-Quinn Conditions.- Systems Satisfying the Conditions of LaSalle.- Time-Varying Case.- Strictification: Basic Results.- Backstepping for Time-Varying Systems.- Matrosov Conditions: General Case.- Adaptively Controlled Systems.- Systems with Multiple Time Scales.- Rapidly Time-Varying Systems.- Slowly Time-Varying Systems.- Hybrid Time-Varying Systems.

From the reviews: "This monograph covers a wide range of nonlinear dynamical systems, including Jurdjevic-Quinn systems, time-varying systems satisfying LaSalle or Matrosov conditions, adaptively controlled dynamics, slowly and rapidly time-varying systems, and hybrid time-varying systems. ... The book will be useful to researchers and graduate students in various areas of applied mathematics and control theory and engineering." (Vladimir Sobolev, Zentralblatt MATH, Vol. 1186, 2010) "This is an important and painstaking chore. ... The book is a combination of a research monograph and an expository text. ... those who need to analyze or to perform a detailed stability or stabilization analysis of concrete equations will find the book a very good source of ideas and references. ... should be a desired addition to all libraries that serve mathematics departments and control engineering faculties. ... could be used successfully as reading material for advanced graduate students interested in the subject matter." (Zvi Artstein, SIAM Review, Vol. 53 (1), 2011)

• Background.- Background on Nonlinear Systems.- Review of Lyapunov Functions.- Time-Invariant Case.- Matrosov Conditions: Simple Case.- Jurdjevic-Quinn Conditions.- Systems Satisfying the Conditions of LaSalle.- Time-Varying Case.- Strictification: Basic Results.- Backstepping for Time-Varying Systems.- Matrosov Conditions: General Case.- Adaptively Controlled Systems.- Systems with Multiple Time Scales.- Rapidly Time-Varying Systems.- Slowly Time-Varying Systems.- Hybrid Time-Varying Systems.