In the dynamic system, the abrupt changes
of working environment, failures of sensors or actuators, and the working
points of nonlinear systems can be regarded as the phenomena of time-varying or
stochastic switching, which can be widely found in energy, chemical process,
communication, social network, and other practical systems. Due to these
reasons, the models adopted for the design of control systems are more and more
complicated and specific.
This thesis aims at building new frameworks for the synthesis of the positive time-varying linear systems via geometric programming. Specifically, This thesis will make a deep discussion on two issues of the positive linear systems with the time-varying state: the positive semi-Markov jump linear systems and finite-time control of positive time-varying linear systems. By using the results from the matrix theory on the log-log convexity of the spectral radius of nonnegative matrices and posynomials, the problems are reduced to convex optimization problems under certain regularity conditions on the system matrices and the cost function. Finally, the validity and effectiveness of the proposed results are illustrated by using two examples from real application problems.