Abstract
A novel approach is proposed in this paper to design static output feedback controllers for asymptotically stabilizing continuous-time switched linear systems with minimum mode-dependent average dwell time (MMDADT). This approach adopts an iterative algorithm containing the solution of a traversal algorithm function and three optimization functions, the decision variables of which are established by the sum of squares (SOS) of matrix polynomials. The traversal algorithm function takes advantage of a polynomially parameter-bounded condition, allowing us to get the lower-bound of the Homogeneous Polynomial Lyapunov Functions’ (HPLFs) derivative. The first optimization function is a non-convex optimization function, which expresses a sufficient condition for stability analysis and computing MMDADT. The second and third optimization functions are both convex optimization functions, which are used to calculate the polynomially mode-dependent output feedback controllers. Two numerical examples are presented in order to show the feasibility of the proposed results.
Highlights
Switched systems consist of a finite class of subsystems and switching signals which orchestrate the switching rules between each subsystem
vertical take-off and landing (VTOL) unmanned aerial vehicles (UAV), which could transit between vertical and horizontal flight modes, is able to use the approach to design individual controller with minimum mode-dependent average dwell time (MMDADT) to improve the performance of mode switching process with more flexibility and less transition time
A traversal algorithm function gives a means to calculate the minimum value of the modulus of (Ai(κi))’s eigenvalue, ηi∗, by selecting a feasible step size
Summary
Switched systems consist of a finite class of subsystems and switching signals which orchestrate the switching rules between each subsystem. A tactfully new approach to simplifying exponential terms to linear terms and a subsequent exploration of the lower bound of dwell time are necessary, while the switched system is stabilizing Control synthesis is another fundamental issue in timedependent switched systems. VOLUME 7, 2019 function - copositive Lyapunov functions, to solve the problem of stability and stabilization for switched positive linear systems with a MDADT switching strategy In the latter class, linear matrix inequality [30] (LMI), bilinear matrix inequality [31] (BMI) and SOS [32] methods could be formulated to compute the feedback controller on the grounds of conditions proposed in above instances.
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