Invariance in linear systems

Immersion and invariance adaptive control of linear multivariable systems

We show in this paper that it is possible to globally adaptively stabilize linear multivariable systems with reduced prior knowledge of the high-frequency gain. In particular, we relax the restrictive (nongeneric) symmetry condition usually required to solve this problem. Instrumental for the establishment of our result is the use of the new immersion and invariance approach to adaptive control...

Extending LaSalle’s Invariance Principle to Switched Linear Systems

In this paper we extend LaSalle’s Invariance Principle to certain classes of switched linear systems. In particular we illustrated how to prove asymptotic stability using multiple Lyapunov functions whose Lie derivatives are only negative semi-definite.

Invariance of Approximating Automata for Piecewise Linear Systems with Uncertainties

Piecewise linear systems systems that switch between different linear subsystems at different occasions occur in many applications. Due to their nonlinearity, they may often be difficult to analyse. Therefore, different approximating methods have been developed for analysis, verification and control design. This report considers one such method, and gives some algorithms for investigating how s...

Invariance and Stability by State Feedback for Constrained Linear Systems

Distributed Robust Set-Invariance for Interconnected Linear Systems

We introduce a class of distributed control policies for networks of discrete-time linear systems with polytopic additive disturbances. The objective is to restrict the network-level state and controls to userspecified polyhedral sets for all times. This problem arises in many safety-critical applications. We consider two problems. First, given a communication graph characterizing the structure...