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OUTPUT – INPUT STABILITY and FEEDBACK STABILIZATION

OUTPUT – INPUT STABILITY and FEEDBACK STABILIZATION. Daniel Liberzon. Coordinated Science Laboratory and Dept. of Electrical & Computer Eng., Univ. of Illinois at Urbana-Champaign U.S.A. CDC ’03. MOTIVATION. ISS:. stability (no outputs). linear : stable eigenvalues.

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OUTPUT – INPUT STABILITY and FEEDBACK STABILIZATION

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  1. OUTPUT – INPUT STABILITY andFEEDBACK STABILIZATION Daniel Liberzon Coordinated Science Laboratory and Dept. of Electrical & Computer Eng., Univ. of Illinois at Urbana-Champaign U.S.A. CDC ’03

  2. MOTIVATION ISS: stability (no outputs) linear: stable eigenvalues detectability (no inputs) linear: stable unobserv. modes minimum phase linear: stable zeros stable inverse ? ? ?

  3. DEFINITION Example: (L, Sontag, Morse, 2002)Call the system output-input stable if integer N and functions s.t. where

  4. UNDERSTANDING OUTPUT-INPUT STABILITY 1 1 2 2 Uniform detectability w.r.t. extended output: 3 3 Input-bounding property: <=> + Output-input stability:

  5. SISO SYSTEMS For affine systems: this reduces to relative degree ( ) doesn’t have this property For affine systems in global normal form, output-input stability ISS internal dynamics For systems analytic in controls, can replace the input-bounding property by where is the first derivative containing u

  6. MIMO SYSTEMS Input-bounding property: Example: Detectability: Equation for is ISS w.r.t. Existence of vector relative degree not necessary For linear systems reduces to usual minimum phase notion Input-bounding property – via nonlinear structure algorithm

  7. APPLICATION: FEEDBACK DESIGN Output stabilization state stabilization Example: Output-input stability closed-loop GAS No global normal form is needed Global asymptotic stabilization by static state feedback See also Astolfi, Ortega, Rodriguez (2002)

  8. APPLICATIONS of OUTPUT-INPUT STABILITY Potential other applications: • Stabilization & small gain (Jiang, Praly, et. al.) • Output regulation, disturbance decoupling (Isidori) • Bode integrals and entropy (Iglesias) • Bode integrals and cheap control (Seron et. al.) • More ? • Analysis of cascade systems • Adaptive control • Input / output operators See L, Sontag, Morse (TAC 2002), L (MTNS 2002 )

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