Input-to-state stability of infinite-dimensional control systems

Input-to-state stability of infinite-dimensional control systems

We develop tools for investigation of input-to-state stability (ISS) of infinite-dimensional control systems. We show that for certain classes of admissible inputs the existence of an ISS-Lyapunov function implies the inputto-state stability of a system. Then for the case of the systems described by abstract equations in Banach spaces we develop two methods of construction of local and global I...

Characterizations of input-to-state stability for infinite-dimensional systems

We prove characterizations of input-to-state stability (ISS) for a large class of infinite-dimensional control systems, including some classes of evolution equations over Banach spaces, time-delay systems, ordinary differential equations (ODE), switched systems. These characterizations generalize wellknown criteria of ISS, proved by Sontag and Wang for ODE systems. For the special case of diffe...

The Circle Criterion and Input-to-State Stability for Infinite-Dimensional Systems∗

In this paper, the focus is on absolute stability and input-to-state stability of the feedback interconnection of an infinite-dimensional linear system Σ and a nonlinearity Φ : dom(Φ) ⊂ Lloc(R+, Y ) → L 2 loc(R+, U), where dom(Φ) denotes the domain of Φ and U and Y (Hilbert spaces) denote the input and output spaces of Σ, respectively (see Figure 1, wherein v is an essentially bounded input sig...

Input-to-state stability of networked control systems

Stability of infinite dimensional control problems with pointwise state constraints

A general class of nonlinear infinite dimensional optimization problems is considered that covers semi-linear elliptic control problems with distributed control as well as boundary control. Moreover, pointwise inequality constraints on the control and the state are incorporated. The general optimization problem is perturbed by a certain class of perturbations, and we establish convergence of lo...