Liapunov Functions and Stability in Control Theory

1. Front Matter

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2. Differential equations

   Pages 1-17

3. Tine invariant systems

   Pages 19-71

4. Time varying systems

   Pages 73-99

5. Differential inclusions

   Pages 101-143

6. Additional properties of strict Liapunov functions

   Pages 145-180

7. Monotonicity and generalized derivatives

   Pages 181-194

8. Back Matter

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The main purpose of this work is to present a modern and self-contained treatment of the Liapunov method for stability analysis, in the framework of mathematical nonlinear control theory. We focus in particular on the problem of the existence of Liapunov functions (converse Liapunov theorems) and their regularity, whose interest is especially motivated by applications to automatic control (boundedness of state evolution with respect to bounded inputs, stabilization by feedback). Many recent results in this area have been collected and presented in a systematic way. Some of them are given in extended, unified versions and with new, simpler proofs.

• Direct Liapunov Method
• Lyapunoc Function
• Nonlinear Systems
• control
• control theory
• differential inclusions
• nonlinear control
• nonlinear system
• stability
• stabilization

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