Sign Stability Of A Class Of Double-switching Linear System

As a traditional and classical robust stability,sign stability is widely used in various complex systems due to its strong stability and anti-disturbance ability.Compared with the traditional Lyapunov stability control method,it helps to reduce the difficulty of solving linear matrix inequalities.In this paper,the sign stability of dual switching linear systems is studied by applying sign stability to the numerical stability of dual switching linear systems to obtain the qualitative stability of a class of dual switching linear systems.For the dual switching linear continuous-time positive system,its deterministic switching law is designed by using the average dwell time and the pre-set deterministic switching law based on the decay of the energy function,and the stochastic switching obeys the Markov process,and the sufficient conditions of exponentially stability and exponentially mean-square stability are obtained in the form of linear matrix inequalities.Analyzing their respective sufficient conditions,combining the relevant theories of sign stability,the conditions of exponentially sign stability and exponentially mean-square sign stability of the dual switching linear continuous-time positive system are derived,and the equivalence of the two is proved.Generalized from the positive system to the general system,for the dual switching linear continuous-time system,the deterministic switching law is designed by using the method of pre-setting the deterministic switching law based on the decay of the energy function,and the stochastic switching obeys the Markov process,and the sufficient conditions for its exponentially almost-sure stability are obtained in the form of linear matrix inequalities.The sufficient conditions are equivalently analyzed,combining the relevant theories of sign stability,and the conditions of the exponentially almost-sure sign stability of the dual switching linear continuous-time system are derived.The deficiency of the sign stability of the positive system is compensated by modifying its mathematical model,which greatly reduces its conservativeness.