  We investigate the problem of synthesizing switching controllers for
stabilizing continuous-time plants. First, we introduce a class of control
Lyapunov functions (CLFs) for switched systems along with a switching strategy
that yields a closed loop system with a guaranteed minimum dwell time in each
switching mode. However, the challenge lies in automatically synthesizing
appropriate CLFs. Assuming a given fixed form for the CLF with unknown
coefficients, we derive quantified nonlinear constraints whose feasible
solutions (if any) correspond to CLFs for the original system. However, solving
quantified nonlinear constraints pose a challenge to most LMI/BMI-based
relaxations. Therefore, we investigate a general approach called
Counter-Example Guided Inductive Synthesis (CEGIS), that has been widely used
in the emerging area of automatic program synthesis. We show how a LMI-based
relaxation can be formulated within the CEGIS framework for synthesizing CLFs.
We also evaluate our approach on a number of interesting benchmarks, and
compare the performance of the new approach with our previous work that uses
off-the-shelf nonlinear constraint solvers instead of the LMI relaxation. The
results shows synthesizing CLFs by using LMI solvers inside a CEGIS framework
can be a computational feasible approach to synthesizing CLFs.
