A Bounded Real Lemma for nonlinear ℒ2-gain

The well-known Bounded Real Lemma plays a key role in ℒ<inf>2</inf>-gain based control methods such as H<inf>∞</inf> control for both linear and nonlinear systems. Recently, conventional (linear) ℒ<inf>2</inf>-gain concepts have been generalized to the nonlinear ℒ<inf>2</inf>-gain framework to encompass a larger class of systems. A bounded real lemma has been developed corresponding to this generalized notion of nonlinear ℒ<inf>2</inf>-gain.

[1]  Huan Zhang,et al.  Nonlinear ℒ2-gain analysis via a cascade , 2010, 49th IEEE Conference on Decision and Control (CDC).

[2]  Matthew R. James,et al.  A partial differential inequality for dissipative nonlinear systems , 1993 .

[3]  Van,et al.  L2-Gain Analysis of Nonlinear Systems and Nonlinear State Feedback H∞ Control , 2004 .

[4]  Joseph A. Bally,et al.  Viscosity Solutions of Hamilton{jacobi Equations Arising , 1996 .

[5]  Peter M. Dower,et al.  A dynamic programming approach to the approximation of nonlinear L2-gain , 2008, 2008 47th IEEE Conference on Decision and Control.

[6]  J. Quadrat.  Numerical methods for stochastic control problems in continuous time , 1994 .

[7]  Peter M. Dower,et al.  A max-plus approach to the approximation of transient bounds for systems withnonlinear L 2-gain , 2010 .

[8]  Eduardo Sontag,et al.  New characterizations of input-to-state stability , 1996, IEEE Trans. Autom. Control..

[9]  M. Bardi,et al.  Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations , 1997 .

[10]  Zhong-Ping Jiang,et al.  Small-gain theorem for ISS systems and applications , 1994, Math. Control. Signals Syst..

[11]  David J. N. Limebeer,et al.  Linear Robust Control , 1994 .

[12]  Fabian R. Wirth,et al.  Asymptotic stability equals exponential stability, and ISS equals finite energy gain---if you twist your eyes , 1998, math/9812137.

[13]  J. Willems.  Dissipative dynamical systems part I: General theory , 1972 .

[14]  Ian R. Petersen,et al.  A nonsmooth strict bounded real lemma , 2005, Syst. Control. Lett..

[15]  A. Schaft.  L/sub 2/-gain analysis of nonlinear systems and nonlinear state-feedback H/sub infinity / control , 1992 .

[16]  William M. McEneaney,et al.  Max-plus methods for nonlinear control and estimation , 2005 .