Stability of Switched Systems With Partial State Reset

International Journal of Control

Rocha

2016

Self Cite

We study the stability of a certain class of switched systems where discontinuous jumps (resets) on some of the state components are allowed, at the switching instants. It is known that, if all components of the state are available for reset, the system can be stabilizable by an adequate choice of resets. However, this question may have negative answer if there are forbidden state components for reset. We give a sufficient condition for the stabilizability of a switched system, under arbitrary switching, by partial state reset in terms of a block simultaneous triangularizability condition. Based on this sufficient condition, we show that the particular class of systems with partially commuting stable system matrices is stabilizable by partial state reset. We also provide an algorithm that allows testing whether a switched system belongs to this particular class of systems.

“…Another result related to the existence of CQLF is the following, see Brás et al (2013) for a proof.…”

Section: Preliminariesmentioning

confidence: 98%

“…A switched system for which only some of the state components may jump during switching is called a switched system with partial state reset, Brás, Carapito, and Rocha (2013).…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Stability of simultaneously block triangularisable switched systems with partial state reset

Brás

International Journal of Control

Rocha

2016

Self Cite

Stabilization criteria of a class of switched systems

Math Methods in App Sciences

2019

In this paper, stabilizability property for a switched system under arbitrary switching is considered from an algebraic point of view by means of the existence of a set of block‐diagonal Lyapunov solutions with common Schur complement of certain order—or, equivalently, with common block (1,1)—for the matrix bank. It is shown that the existence of that set is equivalent to the existence of solutions for some Riccati inequalities done in terms of the blocks of matrices of the bank. In addition, we conclude that a particular class of systems with matrix bank constituted by Metzler matrices—Positive Switched Systems—are stabilizable by partial state reset.

An approach to the stability of reset switched systems using dynamics without reset

Math Methods in App Sciences

Brás

Rocha

2023

Self Cite

In this paper, we consider switched linear systems that have jumps in the state (determined by a reset rule) at each switching instant. Those systems are called switched systems with state reset. We show that it is possible to analyze the state trajectories of a switched system with state reset by considering suitable switched systems without state resets, that is, with continuous state trajectories. We establish sufficient conditions for the stability of switched systems with state reset using the associated systems without reset. Moreover, introducing some restrictions, we also derive simple algebraic stability conditions. The obtained results are used in numerical examples to show the effectiveness of the proposed approach.