By a switched system, we mean hybrid dynamical system consisting of family continuous-time subsystems and rule that orchestrates the switching between them. The article surveys developments in three basic problems regarding stability design systems. These are: for arbitrary sequences, certain useful classes construction stabilizing sequences. We also provide motivation studying these by discussing how they arise connection with various questions interest control theory applications.

This paper addresses feedback stabilization problems for linear time-invariant control systems with saturating quantized measurements. We propose a new design methodology, which relies on the possibility of changing sensitivity quantizer while system evolves. The equation that describes evolution time (discrete rather than continuous in most cases) is interconnected given (either or discrete), resulting hybrid system. When applied to are stabilizable by feedback, this approach yields global...

We present a sufficient condition for asymptotic stability of switched linear system in terms the Lie algebra generated by individual matrices. Namely, if this is solvable, then exponentially stable arbitrary switching. In fact, we show that any family systems satisfying possesses quadratic common Lyapunov function. also discuss implications result nonlinear systems.

This note is concerned with the problem of stabilizing a nonlinear continuous-time system by using sampled encoded measurements state. We demonstrate that global asymptotic stabilization possible if suitable relationship holds between number values taken encoder, sampling period, and parameter, provided feedback law achieving input-to-state stability respect to measurement errors can be found. The issue relaxing latter condition also discussed.

We consider the problem of stabilizing a linear time-invariant system using sampled encoded measurements its state or output. derive relationship between number values taken by encoder and norm transition matrix open-loop over one sampling period, which guarantees that global asymptotic stabilization can be achieved. A coding scheme control strategy are described explicitly.

It was recently shown that a family of exponentially stable linear systems whose matrices generate solvable Lie algebra possesses quadratic common Lyapunov function, which implies the corresponding switched system is for arbitrary switching. In this paper we prove same properties hold under weaker condition generated by given can be decomposed into sum ideal and subalgebra with compact group. The local stability result nonlinear also established. Moreover, demonstrate if fails to satisfy...

This work proposes several definitions of "norm-observability" for nonlinear systems and explores relationships among them. These observability properties involve the existence a bound on norm state in terms norms output input some time interval. A Lyapunov-like sufficient condition norm-observability is also obtained. As an application, we prove variants LaSalle's stability theorem switched systems. results are demonstrated to be useful control design presence switching as well developing...

We consider the problem of achieving input-to-state stability (ISS) with respect to external disturbances for control systems linear dynamics and quantized state measurements. Quantizers considered in this paper take finitely many values have an adjustable "zoom" parameter. Building on approach applied previously no disturbances, we develop a methodology that counteracts unknown disturbance by switching repeatedly between "zooming out" in." Two specific strategies yield ISS are presented....

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> We generalize and unify a range of recent results in quantized control systems (QCS) networked (NCS) literature provide unified framework for controller design with quantization time scheduling via an emulation-like approach. A crucial step our proofs is finding appropriate Lyapunov function the quantization/time-scheduling protocol which verifies its uniform global exponential stability (UGES)....

Abstract This paper addresses the problem of controlling a continuous‐time linear system with large modelling errors. We employ an adaptive control algorithm consisting family candidate controllers supervised by high‐level switching logic. Methods for constructing such controller families have been discussed in recent authors. The present concentrates on task multiple model context. describe and compare two different logics, each case study behaviour resulting closed‐loop hybrid system....

We consider the problem of determining an appropriate model set on which to design a controllers for multiple switching adaptive control scheme. show that, given mild assumptions uncertainty linear time-invariant plant models, it is possible determine finite such that each in set, satisfactory performance will be obtained some controller set. also demonstrate how may found. The analysis exploits Vinnicombe metric and fact approximately band- time-limited transfer functions...

This paper presents a characterization of observability and an observer design method for switched linear systems with state jumps. A necessary sufficient condition is presented observability, globally in time, when the system evolves under predetermined mode transitions. Because this depends upon switching signal consideration, existence singular signals studied alongside developing that guarantees uniform respect to times. Furthermore, while taking jumps into account, relatively weaker...