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Converse Lyapunov function theory guarantees the existence of strict Lyapunov functions in many situations, but the functions it provides are often abstract and nonexplicit, and therefore may not lend themselves to engineering applications. Often, even when a system is known to be stable, one still needs explicit Lyapunov functions; however, once an appropriate strict Lyapunov function has been constructed, many robustness and stabilization problems can be solved through standard feedback designs or robustness arguments. Non-strict Lyapunov functions are often readily constructed.

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This edited book contains selected papers presented at the Louisiana Conference on Mathematical Control Theory (MCT'03), which brought together over 35 prominent world experts in mathematical control theory and its applications. The book forms a well-integrated exploration of those areas of mathematical control theory in which nonsmooth analysis is having a major impact. These include necessary and sufficient conditions in optimal control, Lyapunov characterizations of stability, input-to-state stability, the construction of feedback mechanisms, viscosity solutions of Hamilton-Jacobi...

Converse Lyapunov function theory guarantees the existence of strict Lyapunov functions in many situations, but the functions it provides are often abstract and nonexplicit, and therefore may not lend themselves to engineering applications. Often, even when a system is known to be stable, one still needs explicit Lyapunov functions; however, once an appropriate strict Lyapunov function has been constructed, many robustness and stabilization problems can be solved through standard feedback designs or robustness arguments. Non-strict Lyapunov functions are often readily constructed.

This...