 
Summary: 1
InfiniteHorizon Switched LQR Problems in Discrete Time: A Suboptimal Algorithm With
Performance Analysis
Wei Zhang, Jianghai Hu, and Alessandro Abate
Abstract This paper studies the quadratic regulation problem
for discretetime switched linear systems (DSLQR problem) on
an infinite time horizon. A general relaxation framework is
developed to simplify the computation of the value iterations.
Based on this framework, an efficient algorithm is developed
to solve the infinitehorizon DSLQR problem with guaranteed
closedloop stability and suboptimal performance. Due to its
stability and suboptimal performance guarantees, the proposed
algorithm can be used as a general controller synthesis tool for
switched linear systems.
This paper studies an extension of the classical LQR prob
lem to switched linear systems (SLS), which will be referred
to as the DiscreteTime Switched LQR (DSLQR) Problem.
The goal is to find both the continuouscontrol and switching
control strategies to minimize a quadratic cost functional over
an infinite time horizon. The problem is expected to play a
