A nurse is cаring fоr а client receiving hemоdiаlysis. A nurse is caring fоr a client who has received hemodialysis. Which of the following assessment findings require follow-up? Medical History Nurse's Notes Client has a history of type 2 diabetes mellitus, chronic kidney disease, and hemodialysis with Arteriovenous fistula. Day 1: 1000: Client alert and oriented x3. Lung fields clear, heart rhythm regular; bowel sounds normoactive x4; ate 75% of morning meal. Denies pain. Left forearm arteriovenous (AV) fistula, skin warm, brachial and radial pulses 2+. 1600: Client returned from dialysis, lethargic, not hungry, tried to eat a few crackers but vomited them up. Capillary blood glucose 125 mg/dL. AV fistula site skin warm, bruit and thrill noted, brachial and radial pulses palpable. Day 2: 0700: Client reports not sleeping well last night; capillary blood glucose 95 mg/dL; crackles in left lower lobe; unproductive cough; AV fistula site ecchymotic, warm, bruit and thrill noted. Oriented to person, place, and time. Day 1: 1000: Temperature 36.3°C (97.3°F) Heart rate 70/min Respiratory rate 16/min Blood pressure 144/72 mm Hg Oxygen saturation 94% on room air Weight 90 kg (198 lb) 1600: Temperature 37.1 °C (98.7°F) Heart rate 62/min Respiratory rate 16/min Blood pressure 112/54 mm Hg Oxygen saturation 95% on room air Day 2: 0700: Temperature 36.7°C (98.1°F) Heart rate 62/min Respiratory rate 12/min Blood pressure 118/52 mmHg Oxygen saturation 95% on room air Weight 86.4 kg (190 lb)
Prоblem 1. (20 pts) A nоnlineаr system is given bybegin{аlign*} dоt x_1&=2-x_1-x_2 \ dot x_2&=(x_1-x_2)x_2.end{аlign*} Find all the equilibrium points of the system and determine their local stability, if possible. Problem 2. (20 pts) Consider the continuous-time LTI system x·=-1-110x{"version":"1.1","math":"x·=-1-110x"}. Can you find a quadratic Lyapunov function (V(x)=x^T P x) of it with (Psucc 0)? If yes, find one such (P); if not, explain why. Problem 3. (25 pts) Consider the following discrete-time LTI system: x[k+1]={"version":"1.1","math":"x[k+1]="}11-1-1{"version":"1.1","math":"11-1-1"}x[k]{"version":"1.1","math":"x[k]"}+1-1{"version":"1.1","math":"+1-1"}u[k]{"version":"1.1","math":"u[k]"} (a) (10 pts) Suppose x0={"version":"1.1","math":"x0="}00{"version":"1.1","math":"00"}. Does there exist control (u[0],u[1]) such that x2={"version":"1.1","math":"x2="}11{"version":"1.1","math":"11"}? If so, find one such control (u[0],u[1]); otherwise, state your reason. (b) (10 pts) Suppose x[0]={"version":"1.1","math":"x[0]="}11{"version":"1.1","math":"11"} . Does there exist control (u[0],u[1]) such that x[2]={"version":"1.1","math":"x[2]="}00{"version":"1.1","math":"00"}? If so, find one such control (u[0],u[1]); otherwise, state your reason. (c) (5 pts) Construct a state variable transformation (T) so that in the new coordinates, the reachable part is separated from the non-reachable part in the transformed system ((tilde A,tilde B)). Problem 4. (15 pts) A discrete-time LTI system (x[k+1]=Ax[k]+Bu[k]) is given with A=-1101, B=01{"version":"1.1","math":"A=-1101, B=01"}Suppose (x[0]=0) and the goal is to have x[3]=1-1T{"version":"1.1","math":"x[3]=1-1T"}. Find the control inputs (u[0],u[1],u[2]) with the minimum energy (|u[0]|^2+|u[1]|^2+|u[2]|^2) that achieves the goal. Problem 5. (20 pts) Consider the following system ((alpha,beta in mathbb R) are constants):[ x[k+1] = begin{bmatrix} 1& 0\-1&1end{bmatrix} x[k], quad y[k]=begin{bmatrix} alpha &betaend{bmatrix} x[k].] (a) (5 pts) Find the condition that (alpha) and (beta) need to satisfy for the system to be observable. (b) (15 pts) Assume (alpha=beta=1). For the following two sets of possible output measurements (assuming no measurement error), determine if each set is feasible for the above given system. If the answer is yes, find the (x[0]) resulting in the output measurements; if the answer is no, explain why.begin{align*} &text{Set (i):};; y[0]=-1,; y[1]=2,; y[2]=5;\ &text{Set (ii):};; y[0]=1,; y[1]=-1,; y[2]=3.end{align*} Congratulations, you are almost done with Midterm Exam 2. DO NOT end the Honorlock session until you have submitted your work to Gradescope. When you have answered all questions: Use your smartphone to scan your answer sheet and save the scan as a PDF. Make sure your scan is clear and legible. Submit your PDF to Gradescope as follows: Email your PDF to yourself or save it to the cloud (Google Drive, etc.). Click this link to go to Gradescope to submit your work: Midterm Exam 2 Return to this window and click the button below to agree to the honor statement. Click Submit Quiz to end the exam. End the Honorlock session.