Guaranteeing Stability of a NCS with a Decentralized State Feedback Controller - Example
This example shows how to find a statefeedback control law with fast convergence.
Contents
ovrapx='JNF'; drpmdl = 'explicit'; lyap = 'pardep';
Define the Network Control System
The plant is a decentralized controller which is given as
with feedback
The subsystem matrices are given as
A1=[0.6 -4.2; 0.1 -2.1]; B1=[0.7 1.9; 0 1]; K1= [1.94 -1.40; -0.56 -0.86]; A2=[-3.2 0.2; 5.3 -0.2]; B2=[0.8; -0.4]; K2 = [1.36 0.81];
and the coupling matrices are given as
Ac1 = [0.1 2.1; 0.01 0]; Ac2 = [0 0; 0 -0.03]; Bc1 = [-0.02; -0.01]; Bc2=[0 0; 0 0];
We can express this as one system with the expression
where
A=[A1 Ac1; Ac2 A2]; B=[B1 Bc1; Bc2 B2]; K= [K1 zeros(2); 0 0 K2];
%plotting options gamma=0; hnom=1; hStep=0.04; tauStep=0.04; taumax=1; taumin=0; % %% % tau=taumin; % hmax=hnom; % hmin=hnom; % %StabReg_lower = [h tau]; % lastStable = 0; % while tau >=taumin && tau <= taumax && tau <=hmin % ncs1 = dncs(A,B,K,[hmin hmax],[taumin tau],0,drpmdl); % [stable, K] = isNcsStable(ncs1,lyap,gamma,ovrapx); % if stable == 1 % figure(1); % plot(hmin,tau,'g.','Markersize',15) % plot(hmax,tau,'g.','Markersize',15) % title('h_{mati}, \tau_{mad} Tradeoff Plot') % xlabel('h_{mati}'); % ylabel('\tau_{mad}'); % hold on; % figure(1); % %StabReg_lower(end+1,:)=[h tau]; % hmin = hmin - hStep; % hmax = hmax + hStep; % elseif stable == 0 % title('h_{mati}, \tau_{mad} Tradeoff Plot') % xlabel('h_{mati}'); % ylabel('\tau_{mad}'); % plot(hmin,tau,'rx') % plot(hmax,tau,'rx') % hold on; % figure(1); % if lastStable == 1 % tau = tau + tauStep; % else % hmin = hmin + hStep; % hmax = hmax - hStep; % end % end % lastStable = stable; % end % % disp('Tradeoff plot COMPLETE!!!')