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COMMON WEAK LYAPUNOV FUNCTIONS and OBSERVABILITY

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Barbashin-Krasovskii-LaSalle theorem: (observability with respect to ) observable ... To handle nonlinear switched systems and. non-quadratic weak Lyapunov functions, ... – PowerPoint PPT presentation

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Title: COMMON WEAK LYAPUNOV FUNCTIONS and OBSERVABILITY


1
COMMON WEAK LYAPUNOV FUNCTIONS and
OBSERVABILITY
Daniel Liberzon
Coordinated Science Laboratory and Dept. of
Electrical Computer Eng., Univ. of Illinois at
Urbana-Champaign
2
OBSERVABILITY and ASYMPTOTIC STABILITY
Barbashin-Krasovskii-LaSalle theorem
is GAS if s.t.
3
Theorem (common weak Lyapunov function)
Switched linear system is GAS if
4
OBSERVABILITY MOTIVATING REMARKS
Several ways to define observability (equivalent
for linear systems)
Benchmarks
  • observer design or state norm estimation
  • detectability vs. observability
  • LaSalles stability theorem for switched systems

Joint work with Hespanha, Sontag, and Angeli
No inputs here, but can extend to systems with
inputs
5
STATE NORM ESTIMATION
This is a robustified version of
0-distinguishability
6
OBSERVABILITY DEFINITION 1 A CLOSER LOOK
7
DETECTABILITY vs. OBSERVABILITY
8
OBSERVABILITY DEFINITION 2 A CLOSER LOOK
Definition
and
Theorem This is equivalent to definition 1
(small-time obs.)
9
SWITCHED NONLINEAR SYSTEMS
Theorem (common weak Lyapunov function)
Switched system is GAS if
HespanhaLSontagAngeli 05
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