[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

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

Real and Complex Analysis

This paper studies a number of quantized feedback design problems for linear systems. We consider the case where quantizers are static (memoryless). The common aim of these design problems is to stabilize the given system or to achieve certain performance with the coarsest quantization density. Our main discovery is that the classical sector bound approach is nonconservative for studying these design problems. Consequently, we are able to convert many quantized feedback design problems to well-known robust control problems with sector bound uncertainties. In particular, we derive the coarsest quantization densities for stabilization for multiple-input-multiple-output systems in both state feedback and output feedback cases; and we also derive conditions for quantized feedback control for quadratic cost and H/sub /spl infin// performances.

The sector bound approach to quantized feedback control | NOVA. The University of Newcastle's Digital Repository

Stability and L2-gain analysis for switched delay systems: A delay-dependent method

This correspondence considers the stability problem for a class of linear switched systems with time-varying delay in the sense of Hurwitz convex combination. The bound of derivative of the time-varying delay can be an unknown constant. It is concluded that the stability result for linear switched systems still holds for such systems with time-varying delay under a certain delay bound. Moreover, the delay bound of guaranteeing system stability can be easily obtained based on linear matrix inequalities (LMIs). As a special case, when the time-varying delay becomes constant, the criterion obtained in this correspondence is less conservative than existing ones. The reason for less conservativeness is also explicitly explained in this correspondence. Simulation examples illustrate the effectiveness of the proposed method.

Stability Analysis for Linear Switched Systems With Time-Varying Delay

Integral input-to-state stability for hybrid delayed systems with unstable continuous dynamics

This paper studies the stability for a class of systems with time-varying delay subject to controller failure. It explores under what conditions of controller failure the system is still exponentially stable. The concept of controller failure frequency is introduced. First, the delay system with failed controller is modelled as a class of switched delay systems. Next, based on two lemmas developed in this paper and the piecewise Lyapunov functional method, sufficient conditions are provided to guarantee the exponential stability of the system when controller failure occurs, which is in terms of the solvability of a set of linear matrix inequalities (LMIs). Finally, an example of a networked control system is given to illustrate the effectiveness of the proposed method.

Xi-Ming Sun

Papers

Stability and L2-gain analysis for switched delay systems: A delay-dependent method

Stability Analysis for Linear Switched Systems With Time-Varying Delay

Integral input-to-state stability for hybrid delayed systems with unstable continuous dynamics

Stability of Systems With Controller Failure and Time-Varying Delay

Brief paper: Delay-dependent stability for discrete systems with large delay sequence based on switching techniques