Input-to-state stability (ISS)[1][2][3][4][5][6] is a stability notion widely used to study stability of nonlinear control systems with external inputs. Roughly speaking, a control system is ISS if it is globally asymptotically stable in the absence of external inputs and if its trajectories are bounded by a function of the size of the input for all sufficiently large times. The importance of ISS is due to the fact that the concept has bridged the gap between input–output and state-space methods, widely used within the control systems community.
ISS unified the Lyapunov and input-output stability theories and revolutionized our view on stabilization of nonlinear systems, design of robust nonlinear observers, stability of nonlinear interconnected control systems, nonlinear detectability theory, and supervisory adaptive control. This made ISS the dominating stability paradigm in nonlinear control theory, with such diverse applications as robotics, mechatronics, systems biology, electrical and aerospace engineering, to name a few.
The notion of ISS was introduced for systems described by ordinary differential equations by Eduardo Sontag in 1989.[7]
Since that the concept was successfully used for many other classes of control systems including systems governed by partial differential equations, retarded systems, hybrid systems, etc.[5]
- ^ Eduardo D. Sontag. Mathematical Control Theory: Finite-Dimensional Systems. Springer-Verlag, London, 1998
- ^ Hassan K. Khalil. Nonlinear Systems. Prentice Hall, 2002.
- ^ Cite error: The named reference
KaJ11was invoked but never defined (see the help page). - ^ Cite error: The named reference
Son08was invoked but never defined (see the help page). - ^ a b A. Mironchenko, Ch. Prieur. Input-to-state stability of infinite-dimensional systems: recent results and open questions. SIAM Review, 62(3):529–614, 2020.
- ^ Andrii Mironchenko. Input-to-state stability. Springer, 2023.
- ^ Eduardo D. Sontag. Smooth stabilization implies coprime factorization. IEEE Trans. Autom. Control, 34(4):435–443, 1989.
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