A MAXIMUM PRINCIPLE FOR THE STABILITY ANALYSIS OF POSITIVE BILINEAR CONTROL SYSTEMS WITH APPLICATIONS TO POSITIVE LINEAR SWITCHED SYSTEMS

作者：Fainshil Lior; Margaliot Michael^*

来源：SIAM Journal on Control and Optimization, 2012, 50(4): 2193-2215.

DOI：10.1137/11083808X

• positive linear switched systems
• stability under arbitrary switching law
• positive linear systems
• Metzler matrix
• variational approach
• Perron-Frobenius theory
• positive absolute stability problem

We consider a continuous-time bilinear control system (BCS) with Metzler matrices. Each entry in the transition matrix of such a system is nonnegative, making the positive orthant an invariant set of the dynamics. Motivated by the stability analysis of positive linear switched systems (PLSSs), we define a control as optimal if, for a fixed final time, it maximizes the spectral radius of the transition matrix. Our main result is a first-order necessary condition for optimality in the form of a maximum principle (MP). The proof of this MP combines the standard needle variation with a basic result from the Perron-Frobenius theory of nonnegative matrices. We describe several applications of this MP to the stability analysis of PLSSs under arbitrary switching.

• 出版日期2012