There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解

Two types of nonlinear control algorithms are presented for uncertain linear plants. Controllers of the first type are stabilizing polynomial feedbacks that allow to adjust a guaranteed convergence time of system trajectories into a prespecified neighborhood of the origin independently on initial conditions. The control design procedure uses block control principles and finite-time attractivity properties of polynomial feedbacks. Controllers of the second type are modifications of the second order sliding mode control algorithms. They provide global finite-time stability of the closed-loop system and allow to adjust a guaranteed settling time independently on initial conditions. Control algorithms are presented for both single-input and multi-input systems. Theoretical results are supported by numerical simulations.

https://hal.inria.fr/hal-00757561/document

Nonlinear Feedback Design for Fixed-Time Stabilization of Linear Control Systems

This paper presents control and coordination algorithms for groups of vehicles. The focus is on autonomous vehicle networks performing distributed sensing tasks where each vehicle plays the role of a mobile tunable sensor. The paper proposes gradient descent algorithms for a class of utility functions which encode optimal coverage and sensing policies. The resulting closed-loop behavior is adaptive, distributed, asynchronous, and verifiably correct.

Coverage control for mobile sensing networks

Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)

We introduce a concept of input-to-output practical stability (IOpS) which is a natural generalization of input-to-state stability proposed by Sontag. It allows us to establish two important results. The first one states that the general interconnection of two IOpS systems is again an IOpS system if an appropriate composition of the gain functions is smaller than the identity function. The second one shows an example of gain function assignment by feedback. As an illustration of the interest of these results, we address the problem of global asymptotic stabilization via partial-state feedback for linear systems with nonlinear, stable dynamic perturbations and for systems which have a particular disturbed recurrent structure.

Small-gain theorem for ISS systems and applications

http://math.fau.edu/wang/pdf-file/journal/dt-iss-automatica.pdf

Input-to-state stability for discrete-time nonlinear systems

https://ris.utwente.nl/ws/files/7041947/Jiang97tracking.pdf

Zhong-Ping Jiang

Papers

Small-gain theorem for ISS systems and applications

Input-to-state stability for discrete-time nonlinear systems

Tracking control of mobile robots: a case study in backstepping

Computational adaptive optimal control for continuous-time linear systems with completely unknown dynamics

Design of Robust Adaptive Controllers for Nonlinear Systems with Dynamic Uncertainties