Stabilizing Randomly Switched Systems

This article is concerned with stability analysis and stabilization of randomly switched systems under a class of switching signals. The switching signal is modeled as a jump stochastic (not necessarily Markovian) process independent of the system state; it selects, at each instant of time, the active subsystem from a family of systems. Sufficient conditions for stochastic stability (almost sure, in the mean, and in probability) of the switched system are established when the subsystems do not possess control inputs, and not every subsystem is required to be stable. These conditions are employed to design stabilizing feedback controllers when the subsystems are affine in control. The analysis is carried out with the aid of multiple Lyapunov-like functions, and the analysis results together with universal formulae for feedback stabilization of nonlinear systems constitute our primary tools for control designComment: 22 pages. Submitte

Tools for Stability of Switching Linear Systems: Gain Automata and Delay Compensation.

The topic of this paper is the analysis of stability for a class of switched linear systems, modeled by hybrid automata. In each location of the hybrid automaton the dynamics is assumed to be linear and asymptotically stable; the guards on the transitions are hyperplanes in the state space. For each location an estimate is made of the gain via a Lyapunov function for the dynamics in that location, given a pair of ingoing and outgoing transitions. It is shown how to obtain the best possible estimate by optimizing the Lyapunov function. The estimated gains are used in defining a so-called gain automaton that forms the basis of an algorithmic criterion for the stability of the hybrid automaton. The associated gain automaton provides a systematic tool to detect potential sources of instability as well as an indication on to how to stabilize the hybrid systems by requiring appropriate delays for specific transitions

Stability Analysis for Hybrid Automata Using Conservative Gains

This paper presents a stability analysis approach for a class of hybrid\ud automata. It is assumed that the dynamics in each location of the hybrid automaton is linear and asymptotically stable, and that the guards on the transitions are hyperplanes in the state space. For each pair of ingoing and outgoing transitions in a location a conservative estimate is made of the gain via a Lyapunov function for the dynamics in that location. It is shown how the choice of the Lyapunov function can be optimized to obtain the best possible estimate. The calculated conservative gains are used in defining a so-called gain automaton that forms the basis of an algorithmic criterion for the stability of the hybrid automaton

Loss of the tumor suppressor, Tp53, enhances the androgen receptor-mediated oncogenic transformation and tumor development in the mouse prostate.

Recent genome analysis of human prostate cancers demonstrated that both AR gene amplification and TP53 mutation are among the most frequently observed alterations in advanced prostate cancer. However, the biological role of these dual genetic alterations in prostate tumorigenesis is largely unknown. In addition, there are no biologically relevant models that can be used to assess the molecular mechanisms for these genetic abnormalities. Here, we report a novel mouse model, in which elevated transgenic AR expression and Trp53 deletion occur simultaneously in mouse prostatic epithelium to mimic human prostate cancer cells. These compound mice developed an earlier onset of high-grade prostatic intraepithelial neoplasia and accelerated prostate tumors in comparison with mice harboring only the AR transgene. Histological analysis showed prostatic sarcomatoid and basaloid carcinomas with massive squamous differentiation in the above compound mice. RNA-sequencing analyses identified a robust enrichment of the signature genes for human prostatic basal cell carcinomas in the above prostate tumors. Master regulator analysis revealed SOX2 as a transcriptional regulator in prostatic basal cell tumors. Elevated expression of SOX2 and its downstream target genes were detected in prostatic tumors of the compound mice. Chromatin immunoprecipitation analyses implicate a coregulatory role of AR and SOX2 in the expression of prostatic basal cell signature genes. Our data demonstrate a critical role of SOX2 in prostate tumorigenesis and provide mechanistic insight into prostate tumor aggressiveness and progression mediated by aberrant AR and p53 signaling pathways